The next-to-minimal weights of binary projective Reed-Muller codes
Information Theory
2017-01-09 v1 Algebraic Geometry
math.IT
Abstract
Projective Reed-Muller codes were introduced by Lachaud, in 1988 and their dimension and minimum distance were determined by Serre and S{\o}rensen in 1991. In coding theory one is also interested in the higher Hamming weights, to study the code performance. Yet, not many values of the higher Hamming weights are known for these codes, not even the second lowest weight (also known as next-to-minimal weight) is completely determined. In this paper we determine all the values of the next-to-minimal weight for the binary projective Reed-Muller codes, which we show to be equal to the next-to-minimal weight of Reed-Muller codes in most, but not all, cases.
Cite
@article{arxiv.1701.01658,
title = {The next-to-minimal weights of binary projective Reed-Muller codes},
author = {Cícero Carvalho and Victor G. L. Neumann},
journal= {arXiv preprint arXiv:1701.01658},
year = {2017}
}
Comments
10 pages, Published in IEEE Transactions on Information Theory, vol. 62, issue 11, Nov. 2016