Article

# Optimal self-dual codes over F2×F2 with respect to the Hamming weight

Dept. of Bus. Inf. Sci., Jobu Univ., Gunma, Japan

IEEE Transactions on Information Theory (Impact Factor: 2.62). 03/2004; DOI: 10.1109/TIT.2003.822576 Source: IEEE Xplore

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**ABSTRACT:**The Gleason–Pierce–Ward theorem gives constraints on the divisor and field size of a linear divisible code over a finite field whose dimension is half of the code length. This result is a departure point for the study of self-dual codes. In recent years, additive codes have been studied intensively because of their use in additive quantum codes. In this work, we generalize the Gleason–Pierce–Ward theorem on linear codes over GF(q), q = p m , to additive codes over GF(q). The first step of our proof is an application of a generalized upper bound on the dimension of a divisible code determined by its weight spectrum. The bound is proved by Ward for linear codes over GF(q), and is generalized by Liu to any code as long as the MacWilliams identities are satisfied. The trace map and an analogous homomorphism ${x\mapsto x-x^p}$ on GF(q) are used to complete our proof.Designs Codes and Cryptography 01/2009; 52(3). · 0.78 Impact Factor -
##### Article: Theta-Cyclic Codes Over F2 + vF2

Australasian Journal of Combinatorics 10/2012; 54:115-126. - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper we give the structure of the ternary image of self-dual linear block codes and cyclic linear block codes over the semi-local Frobenius ring R3 = F3 + vF3, where v 2 = 1, with respect to an ordered basis. Sufficient conditions for the ternary image of an R3-code to be of Type III or cyclic are presented.Philippine Computing Journal 01/2012; 7(2):33-37.

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