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The joint weight enumerator of an LCD code and its dual

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Bibliographic Details
Title: The joint weight enumerator of an LCD code and its dual
Authors: Dutour Sikirić, Mathieu
Source: Discrete applied mathematics. 257:12-18
Publisher Information: 2019.
Publication Year: 2019
Subject Terms: Linear binary code, Linear programming bounds, LCD code
Description: A binary linear code is called LCD if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on the size of an LCD code of given length and minimum distance. In addition, we show that this polynomial is, in general, an invariant of a matrix group of dimension 4 and order 12. Also, we sketch a Gleason formula for this weight enumerator.
Document Type: Other literature type
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.10.03210.1016/j.dam.2018.10.032
Accession Number: edsair.dris...01492..29edb068e4db713e658c1c866e63de6e
Database: OpenAIRE
Description
Abstract:A binary linear code is called LCD if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on the size of an LCD code of given length and minimum distance. In addition, we show that this polynomial is, in general, an invariant of a matrix group of dimension 4 and order 12. Also, we sketch a Gleason formula for this weight enumerator.
ISSN:0166218X
DOI:10.1016/j.dam.2018.10.03210.1016/j.dam.2018.10.032