On the size of maximal binary codes with 2, 3, and 4 distances

Alexander Barg; Alexey Glazyrin; Wei Jiun Kao; Ching Yi Lai; Pin Chieh Tseng; Wei Hsuan Yu

doi:10.5070/C64163844

On the size of maximal binary codes with 2, 3, and 4 distances

Alexander Barg
, Alexey Glazyrin
, Wei Jiun Kao
, Ching Yi Lai
, Pin Chieh Tseng
, Wei Hsuan Yu

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n ≥ 6 as well as the exact size of maximal binary constant weight codes with 2, 3, and 4 distances for several values of the weight and for all but small lengths.

Original language	English
Article number	#7
Journal	Combinatorial Theory
Volume	4
Issue number	1
DOIs	https://doi.org/10.5070/C64163844
State	Published - 2024

Keywords

Delsarte inequalities
Erdӧs–Ko–Rado
Johnson space

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10.5070/C64163844

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title = "On the size of maximal binary codes with 2, 3, and 4 distances",

abstract = "We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n ≥ 6 as well as the exact size of maximal binary constant weight codes with 2, 3, and 4 distances for several values of the weight and for all but small lengths.",

keywords = "Delsarte inequalities, Erdӧs–Ko–Rado, Johnson space",

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AU - Barg, Alexander

AU - Glazyrin, Alexey

AU - Kao, Wei Jiun

AU - Lai, Ching Yi

AU - Tseng, Pin Chieh

AU - Yu, Wei Hsuan

N1 - Publisher Copyright: © The authors.

PY - 2024

Y1 - 2024

N2 - We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n ≥ 6 as well as the exact size of maximal binary constant weight codes with 2, 3, and 4 distances for several values of the weight and for all but small lengths.

AB - We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n ≥ 6 as well as the exact size of maximal binary constant weight codes with 2, 3, and 4 distances for several values of the weight and for all but small lengths.

KW - Delsarte inequalities

KW - Erdӧs–Ko–Rado

KW - Johnson space

UR - https://www.scopus.com/pages/publications/85198843673

U2 - 10.5070/C64163844

DO - 10.5070/C64163844

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AN - SCOPUS:85198843673

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VL - 4

JO - Combinatorial Theory

JF - Combinatorial Theory

IS - 1

M1 - #7

ER -

On the size of maximal binary codes with 2, 3, and 4 distances

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Keywords

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