Cyclic codes and self-dual codes over F2 uF2

Abstract

We introduce linear cyclic codes over the ring F2 + uF2 = {0, 1, u, ū= u + 1}, where u2 = 0 and study them by analogy with the Zu case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z4 -codes. Unlike the Z4 case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-dual codes through a linear Gray map. © 1999 IEEE.