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Some Results on Incorrigible Sets of Binary Linear Codes

Hedong HOU, Haiyang LIU, Lianrong MA

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Summary :

In this letter, we consider the incorrigible sets of binary linear codes. First, we show that the incorrigible set enumerator of a binary linear code is tantamount to the Tutte polynomial of the vector matroid induced by the parity-check matrix of the code. A direct consequence is that determining the incorrigible set enumerator of binary linear codes is #P-hard. Then for a cycle code, we express its incorrigible set enumerator via the Tutte polynomial of the graph describing the code. Furthermore, we provide the explicit formula of incorrigible set enumerators of cycle codes constructed from complete graphs.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.2 pp.582-586
Publication Date
2021/02/01
Publicized
2020/08/06
Online ISSN
1745-1337
DOI
10.1587/transfun.2020EAL2021
Type of Manuscript
LETTER
Category
Coding Theory

Authors

Hedong HOU
  Tsinghua University
Haiyang LIU
  the Institute of Microelectronics of Chinese Academy of Sciences
Lianrong MA
  Tsinghua University

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