Title :
Cyclic codes and self-dual codes over F2+uF2
Author :
Bonnecaze, A. ; Udaya, P.
Author_Institution :
GECT, Toulon Univ., La Garde, France
fDate :
5/1/1999 12:00:00 AM
Abstract :
We introduce linear cyclic codes over the ring F2+uF 2={0,1,u,u¯=u+1}, where u2=0 and study them by analogy with the Z4 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
Keywords :
binary codes; cyclic codes; dual codes; linear codes; Z4-codes; alphabet; code structure; extremal self-dual codes; free codes; integer rings; linear Gray map; linear cyclic codes; nonfree codes; odd length code; optimal binary linear codes; self-dual codes; Binary codes; Cities and towns; Galois fields; Information theory; Lattices; Linear code; Mathematics; Modular construction; Polynomials; Reactive power;
Journal_Title :
Information Theory, IEEE Transactions on
