MacWilliams Identities for $m$-tuple Weight Enumerators
Information Theory
2017-06-13 v2 Combinatorics
math.IT
Abstract
Since MacWilliams proved the original identity relating the Hamming weight enumerator of a linear code to the weight enumerator of its dual code there have been many different generalizations, leading to the development of -tuple support enumerators. We prove a generalization of theorems of Britz and of Ray-Chaudhuri and Siap, which build on earlier work of Kl{\o}ve, Shiromoto, Wan, and others. We then give illustrations of these -tuple weight enumerators.
Cite
@article{arxiv.1205.1277,
title = {MacWilliams Identities for $m$-tuple Weight Enumerators},
author = {Nathan Kaplan},
journal= {arXiv preprint arXiv:1205.1277},
year = {2017}
}
Comments
17 pages. Accepted to SIAM Journal on Discrete Mathematics