Title :
On the formal duals of Kerdock codes
Author_Institution :
Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France
fDate :
27 Jun-1 Jul 1994
Abstract :
Recently a new notion was introduced on binary codes, called Z4-linearity, which explains why Kerdock codes and Delsarte-Goethals codes admit formal duals in spite of their nonlinearity. The “Z4-duals” of these codes are new nonlinear codes which admit simpler decoding algorithms than the previously known formal duals. But their characterizations by means of algebraic equations are more complex. We give simpler algebraic characterizations of those codes. We next prove that the relationship between any Z4-linear code and its Z4-dual is stronger than the standard formal duality and deduce the weight enumerators of related generalized codes
Keywords :
algebra; decoding; dual codes; Delsarte-Goethals codes; Kerdock codes; Z4-linear code; Z4-linearity; algebraic characterizations; algebraic equations; binary codes; decoding algorithms; formal duals; generalized codes; nonlinear codes; weight enumerators; Binary codes; Code standards; Decoding; Linear code; Linearity; Optical wavelength conversion; Polynomials;
Conference_Titel :
Information Theory, 1994. Proceedings., 1994 IEEE International Symposium on
Conference_Location :
Trondheim
Print_ISBN :
0-7803-2015-8
DOI :
10.1109/ISIT.1994.395043
