Maximum weight spectrum codes with reduced length
Information Theory
2018-06-15 v1 math.IT
Abstract
A q-ary linear code of dimension k is called a maximum weight spectrum (MWS) code if it has the maximum possible number (viz. (q^k-1)/(q-1)) of different non-zero weights. We construct MWS codes from quasi-minimal codes, thus obtaining of much shorter length than hitherto known. By an averaging argument, we show the existence of MWS codes of even shorter length.
Cite
@article{arxiv.1806.05427,
title = {Maximum weight spectrum codes with reduced length},
author = {Gerard D Cohen and Ludo Tolhuizen},
journal= {arXiv preprint arXiv:1806.05427},
year = {2018}
}
Comments
The second author dedicates this manuscript to the memory of Gerard Cohen, who sadly passed away during its preparation