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: 2.65). 03/2004; DOI: 10.1109/TIT.2003.822576 Source: IEEE Xplore

- [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we investigate the structure and properties of cyclic codes over the ring F2 + vF2. We first study the relationship between cyclic codes over F2 + vF2 and binary cyclic codes. Then we prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over the ring. Finally, we obtain the unique idempotent generators for cyclic codes of odd length and determine the number of cyclic codes for a given length n over F2 + vF2.IEEE Transactions on Information Theory 04/2010; 56(4):1680-1684. · 2.65 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this study, we consider linear and especially cyclic codes over the non-chain ring Zp[v]/⟨vp − v⟩ where p is a prime. This is a generalization of the case p = 3. Further, in this work the structure of constacyclic codes are studied as well. This study takes advantage mainly from a Gray map which preserves the distance between codes over this ring and p-ary codes and moreover this map enlightens the structure of these codes. Furthermore, a MacWilliams type identity is presented together with some illustrative examples.Journal of Algebra Combinatorics Discrete Structures and Applications. 08/2014; 1(1):1-12. - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper quadratic residue codes over the ring Fp+vFpFp+vFp are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes enjoy similar properties as quadratic residue codes over finite fields. For the case p=2p=2, Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes are considered and two optimal Hermitian self-dual codes are obtained as examples. Moreover, a substantial number of good p -ary codes are obtained as images of quadratic residue codes over Fp+vFpFp+vFp in the cases where p is an odd prime. These results are presented in tables.Journal of Pure and Applied Algebra 01/2014; 218(11):1999–2011. · 0.58 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.