Construction of Additive Reed-Muller Codes
Information Theory
2011-12-30 v2 math.IT
Abstract
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of Z2Z4-additive codes such that, under the Gray map, the corresponding binary codes have the same parameters and properties as the usual binary linear Reed-Muller codes. Moreover, the first family is the usual binary linear Reed-Muller family.
Cite
@article{arxiv.0909.3185,
title = {Construction of Additive Reed-Muller Codes},
author = {J. Pujol and J. Rifà and L. Ronquillo},
journal= {arXiv preprint arXiv:0909.3185},
year = {2011}
}
Comments
7 pages, Part of the material in this paper was presented without proofs at the 18-th Symposium on Applied algebra, Algebraic algorithms, and Error Correcting Codes (AAECC 2009), Tarragona, Spain, June 8-12, 2009