English

Rank-metric codes

Information Theory 2019-02-08 v1 math.IT

Abstract

This is a chapter of the upcoming "A Concise Encyclopedia of Coding Theory", W.C. Huffman, J.-L. Kim, and P. Sole' Eds., CRC Press. The chapter gives an introduction to the mathematical theory of rank-metric codes. Treated topics include: definition of rank metric, equivalence of codes, support of a codeword and of a code, duality, weight enumerators and MacWilliams identities, higher rank weights, MRD codes, optimal anticodes, and q-polymatroids associated to a rank-metric code.

Keywords

Cite

@article{arxiv.1902.02650,
  title  = {Rank-metric codes},
  author = {Elisa Gorla},
  journal= {arXiv preprint arXiv:1902.02650},
  year   = {2019}
}

Comments

26 pages, to appear in "A Concise Encyclopedia of Coding Theory", W.C. Huffman, J.-L. Kim, and P. Sole' Eds., CRC Press

R2 v1 2026-06-23T07:34:37.346Z