Lee weights of cyclic self-dual codes over Galois rings of characteristic p2

https://doi.org/10.1016/j.ffa.2016.11.015Get rights and content
Under an Elsevier user license
open archive

Abstract

We completely determine the minimum Lee weights of cyclic self-dual codes over a Galois ring GR(p2,m) of length pk, where m and k are positive integers and p is a prime number. We obtain all cyclic self-dual codes over GR(22,1)Z4 of lengths 16 and 32 with their Lee weight enumerators. We also find cyclic self-dual codes over GR(32,1)Z9 (respectively, GR(32,2)) of lengths up to 27 (respectively, 9). Most of the cyclic self-dual codes we found are extremal with respect to the Lee weights.

MSC

94B15

Keywords

Cyclic code
Self-dual code
Galois ring
Minimum Lee weight
Extremal code

Cited by (0)

1

The author is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827) and also by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (2014-002731).