Cyclic codes over a linear companion of Z4

Abstract

We introduce linear cyclic codes over the ring R=F2/+uF 2={0,1,u,u~=u+1}, where u2/=0. This ring shares many properties of Z4 and F4 and admits a linear «Gray map». Self-dual cyclic codes of odd length exists as in the case of Z 4-codes. We give a BCH-like bound for these codes and describe a simple algebraic decoding procedure. © 1998 IEEE.