English

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 mm-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 mm-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

R2 v1 2026-06-21T20:59:21.975Z