REAL

Binary linear codes with near-extremal maximum distance

Pongrácz, András (2020) Binary linear codes with near-extremal maximum distance. SIAM JOURNAL ON DISCRETE MATHEMATICS. ISSN 0895-4801 (print); 1095-7146 (online) (In Press)

[img]
Preview
Text
AP_SIAM_smalldist.pdf

Download (330kB) | Preview

Abstract

Let C denote a binary linear code with length n all of whose coordinates are essential, i.e., for each coordinate there is a codeword that is not zero in that position. Then the maximum distance D is strictly bigger than n/2, and the extremum D=(n+1)/2 is attained exactly by punctured Hadamard codes. In this paper, we classify binary linear codes with D=n/2+1. All of these codes can be produced from punctured Hadamard codes in one of essentially three different ways, each having a transparent description.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra
Depositing User: Dr. András Pongrácz
Date Deposited: 14 Sep 2020 12:33
Last Modified: 03 Apr 2023 06:54
URI: http://real.mtak.hu/id/eprint/113210

Actions (login required)

Edit Item Edit Item