On the distances of cyclic codes of length 2e over Z4

doi:10.1016/j.disc.2009.07.018

Discrete Mathematics

Volume 310, Issue 1, 6 January 2010, Pages 12-20

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Abstract

Cyclic codes of length $2^{e}$ over $Z_{4}$ are precisely the ideals of the local ring $Z_{4} [x] / 〈 x^{2^{e}} - 1 〉$ . In this paper, we investigate the distances of cyclic codes of length $2^{e}$ over $Z_{4}$ . The Hamming distances of all cyclic codes of length $2^{e}$ over $Z_{4}$ are determined. The exact Lee distances of some cyclic codes of length $2^{e}$ over $Z_{4}$ are also obtained.

Keywords

Cyclic codes

Hamming distances

Lee distances

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^☆: The research is supported by the National Natural Science Foundation of China under Grant No.60673074, College Doctoral Funds of China No.20080359003, and HFUT Research Grant 081003F.

Discrete Mathematics

On the distances of cyclic codes of length 2e over Z4☆

Abstract

Keywords

On the distances of cyclic codes of length $2^{e}$ over $Z_{4}$ ☆