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ABSTRACT: The present research is motivated by the observation that if the period T of a certain binary sequence is a prime, then its linear complexity will be bounded from below by the order of 2 modulo T, i.e., LCOrd
T(2). A class of generators with state periods T(q, n)=q2n–1 are constructed for q=3, 5, 7, 9 and arbitrary n on the basis of a pair of m-sequence generators with the same number of stages, each controlling the clock of the other (bilateral stop-and-go clock control). A new test is derived to find the primes among the numbers T(q, n) with the cases 3 | q and 3 | q treated in a unified manner. The orders of 2 modulo some of the primes T(q, n) are given and some additional cryptographic and implementational remarks are made.
04/2006: pages 194-205;
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ABSTRACT: Most of the research work in the area of algebraic geometric (AG) codes deals with the construction of AG codes from plane algebraic geometric curves. But, some work pertains to the construction of the AG codes from non- planar algebraic geometric curves. However, longer AG codes must have relatively larger genus and should only be the codes constructed from non- planar curves. In this paper, we present a new construction of a class of AG codes from curves in high- dimensional projective spaces. For this construction, it is easy to determine the designed minimum distance and find the parity check matrix, and the decoding up to the designed minimum distance is fast. Furthermore, this approach can be easily understood by most engineers.
01/2006: pages 132-146;
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ABSTRACT: Public-key crypto-algorithms are widely employed for
authentication, signatures, secret-key generation and access
control. The new range of public-key sizes for RSA and
DSA has gone up to 1024 bits and beyond. The elliptic-curve
key range is from 162 bits to 256 bits. Many varied software
and hardware algorithms are being developed for implementation
for smart-card crypto-coprocessors and for public-key
infrastructure. We begin with an algorithm from Aryabhatiya
for solving the indeterminate equation a · x + c =
b · y of degree one (also known as the Diophantine
equation) and its extension to solve the system of two residues
X mod mi = Xi (for i = 1,2). This contribution known
as the Aryabhatiya algorithm (AA) is very profound in the sense that
the problem of two congruences was solved with just one modular
inverse operation and a modular reduction to a smaller modulus
than the compound modulus. We extend AA to any set of t residues, and this is stated as
the Aryabhata remainder theorem (ART). An iterative algorithm is
also given to solve for t moduli mi (i = 1, 2,... ,
t). The ART, which has much in common with the extended
Euclidean algorithm (EEA), Chinese remainder theorem (CRT) and
Garner's algorithm (GA), is shown to have a complexity
comparable to or better than that of the CRT and GA.
Circuits Systems and Signal Processing 01/2006; 25(1):1-15. · 0.82 Impact Factor
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ABSTRACT: In this paper, the cryptanalytic strength of two HwangRao Secret Error-Correcting Code (SECC) schemes is examined under a known-plaintext attack. In particular, we found the existence of key information redundancy in all SECCs used in the electronic codebook (ECB) mode. Also, our investigations indicate the existence of synergism in the SECC schemes, that is, the security of SECC (containing three transformations, # and E and P) is much stronger than the individual strength of either # or E or P. 1
10/2001;
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ABSTRACT: In this paper, the cryptanalytic strength of two Hwang- Rao Secret Error-Correcting Code (SECC) schemes is examined under
a known-plaintext attack. In particular, we found the existence of key information redundancy in all SECCs used in the electronic
codebook (ECB) mode. Also, our investigations indicate the existence of synergism in the SECC schemes, that is, the security of SECC (containing three transformations, Ψ and E and P) is much stronger than the individual strength of either Ψ or E or P.
12/2000: pages 419-428;
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ABSTRACT: A new class of double byte error correcting-triple byte error
detecting (DbEC-TbED) codes over GF(q) is constructed. For the cases of
q=3,4, the new codes are better than the Gilbert-Varshamov bound
Information Theory, 2000. Proceedings. IEEE International Symposium on; 02/2000
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ABSTRACT: Linear error-correcting codes, especially Reed-Solomon codes, find applications in communication and computer memory systems,
to enhance their reliability and data integrity. In this paper, we present Improved Geometric Goppa (IGG) codes, a new class
of error-correcting codes, based on the principles of algebraic-geometry. We also give a reasonably low complexity procedure
for the construction of these IGG codes from Klein curves and Klein-like curves, in plane and high-dimensional spaces. These
codes have good code parameters like minimum distance rate and information rate, and have the potential to replace the conventional
Reed-Solomon codes in most practical applications. Based on the approach discussed in this paper, it might be possible to
construct a class of codes whose performance exceeds the Gilbert-Varshamov bound.
Applicable Algebra in Engineering Communication and Computing 01/2000; 10(6):433-464. · 0.60 Impact Factor
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Appl. Algebra Eng. Commun. Comput. 01/2000; 10:433-464.
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IEEE Transactions on Information Theory 10/1999; 45(6):2209-2209. · 3.01 Impact Factor
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ABSTRACT: The advances information and communications technology, especially
the Internet, have created the opportunity to improve the administrative
efficiency and service quality in governments of many nations. Official
documents in Taiwan are traditionally sent to their corresponding
recipients through the postal service. It has not been possible to
securely transfer official document via the open network using
off-the-shelf e-mail systems. We present our work on integrating
smartcard-based security services (confidentiality, authentication, and
nonrepudiation) into XML-based document exchange systems
Security Technology, 1998. Proceedings., 32nd Annual 1998 International Carnahan Conference on; 11/1998
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ABSTRACT: this paper, the idea of codes from algebraic curves was combined with some recent results from algebraic geometry, to produce a sequence of polynomially constructive error-correcting codes over F q . This led to a new lower bound, the Tsfasman-V ladut-Zink (TVZ) bound, on the information rate of good codes, which is better than the GV bound when q 49. For this paper, the authors received the IEEE Information Theory Group Paper Award in 1983.
08/1998;
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ABSTRACT: The authors study the explicit construction of asymptotically good improved algebraic geometric codes that exceed the Gilbert-Varshamov bound. The also find missing functions in improved well-behaving sequences
Information Theory Workshop, 1998; 07/1998
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ABSTRACT: Double-byte error-correcting codes over GF(q) were constructed by
Dumer (1981, 1988, 1992, 1995), which have the parameters n=q<sup>m-1
</sup>, r⩽2m+[m-1/3], m=2, 3, ..., when q is even, and have the
parameters n=q<sup>m</sup>, r⩽2m+[m/3]+1, m=2; 3, ..., when q is
odd, respectively. We construct a class of double-byte error-correcting
codes over GF(2<sup>i</sup>), which have the following parameters: n=q
<sup>m</sup>, r⩽2m+[m/3]+1, m=3, 4, .... So our constructions reduce
the code redundancy of Dumer by one symbol, and we eliminate the
disparity in code redundancies obtained for even and odd q. A decoding
procedure for our codes is also considered
IEEE Transactions on Information Theory 06/1998; · 3.01 Impact Factor
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ABSTRACT: This paper presents a generalized Bezout theorem which can be used
to determine a tighter lower bound of the number of distinct points of
intersection of two or more plane curves. A new approach to determine a
lower bound on the minimum distance for algebraic-geometric codes
defined from a class of plane curves is introduced, based on the
generalized Bezout theorem. Examples of more efficient linear codes are
constructed using the generalized Bezout theorem and the new approach.
For d=4, the linear codes constructed by the new construction are better
than or equal to the known linear codes. For d⩾5, these new codes
are better than the known AG codes defined from whole spaces. The Klein
codes [22, 16, 5] and [22, 15, 6] over GF(2<sup>3</sup>), and the
improved Hermitian code [64, 56, 6] over GF(2<sup>4</sup>) are also
constructed
IEEE Transactions on Information Theory 12/1997; · 3.01 Impact Factor
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ABSTRACT: The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition.
08/1996;
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ABSTRACT: Error-correcting or error-detecting codes have been used in the computer industry to increase reliability, reduce service costs, and maintain data integrity. The single-byte error-correcting and double-byte error-detecting (SbEC-DbED) codes have been successfully used in computer memory subsystems. There are many methods to construct double-byte error-correcting (DBEC) codes. In the present paper we construct a class of double-byte error-correcting codes, which are more efficient than those known to be optimum, and a decoding procedure for our codes is also considered.
08/1996;
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ABSTRACT: This paper generalizes the previously obtained results to n-dimensional spaces. For n-dimensional spaces, tighter upper bounds on the number of intersection points of two or more polynomials are given. Using the upper bounds, the lower bounds on the minimum distances and the generalized Hamming weights of linear codes defined on the curves in high dimensional spaces are obtained. For large enough h, the exact values of the generalized Hamming weights of linear codes defined on the curves in high dimensional spaces, d(sub h)(C(sub r)), are given. By using the generalized Bezout theorem and the new approach, more efficient linear codes defined on the curves in high dimensional spaces are constructed, which are better than the AG codes and the improved AG codes on the same curves.
08/1996;
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IEEE Transactions on Computers 05/1996; · 1.10 Impact Factor
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ABSTRACT: In this paper, a general method using the subsets (generating
sets) of GF(2<sup>b</sup>) for constructing the SbEC-DED codes will be
presented. The constructions given in Fujiwara and Hamada (1992) are
special cases of ours. For some values of b, the generating sets used in
our constructions are larger than the cosets used in Fujiwara and Hamada
(1992). Hence, a larger code length can be obtained
IEEE Transactions on Computers 05/1996; · 1.10 Impact Factor
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IEEE Transactions on Computers 04/1996; · 1.10 Impact Factor
