Entry-faithful 2-neighbour transitive codes

N.I. Gillespie; Michael Giudici; Dan Hawtin; Cheryl Praeger

doi:10.1007/s10623-015-0069-3

Entry-faithful 2-neighbour transitive codes

N.I. Gillespie, Michael Giudici, Dan Hawtin, Cheryl Praeger

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

8 Citations (Scopus)

Abstract

© 2015, Springer Science+Business Media New York. We consider a code to be a subset of the vertex set of a Hamming graph. The set of (Formula presented.) -neighbours of a code is the set of vertices, not in the code, at distance (Formula presented.) from some codeword, but not distance less than (Formula presented.) from any codeword. A (Formula presented.) -neighbour transitive code is a code which admits a group (Formula presented.) of automorphisms which is transitive on the (Formula presented.) -neighbours, for (Formula presented.) , and transitive on the code itself. We give a classification of (Formula presented.) -neighbour transitive codes, with minimum distance (Formula presented.) , for which (Formula presented.) acts faithfully on the set of entries of the Hamming graph.

Original language	English
Pages (from-to)	549-564
Number of pages	16
Journal	Designs, Codes, and Cryptography
Volume	79
Issue number	3
Early online date	2 Apr 2015
DOIs	https://doi.org/10.1007/s10623-015-0069-3
Publication status	Published - 1 Jun 2016

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10.1007/s10623-015-0069-3

Group Actions: Combinatorics, Geometry and Computation
Praeger, C. (Chief Investigator)
ARC Federation Fellowships
1/01/07 → 31/12/12
Project: Research

Cite this

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title = "Entry-faithful 2-neighbour transitive codes",

abstract = "{\textcopyright} 2015, Springer Science+Business Media New York. We consider a code to be a subset of the vertex set of a Hamming graph. The set of (Formula presented.) -neighbours of a code is the set of vertices, not in the code, at distance (Formula presented.) from some codeword, but not distance less than (Formula presented.) from any codeword. A (Formula presented.) -neighbour transitive code is a code which admits a group (Formula presented.) of automorphisms which is transitive on the (Formula presented.) -neighbours, for (Formula presented.) , and transitive on the code itself. We give a classification of (Formula presented.) -neighbour transitive codes, with minimum distance (Formula presented.) , for which (Formula presented.) acts faithfully on the set of entries of the Hamming graph.",

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T1 - Entry-faithful 2-neighbour transitive codes

AU - Gillespie, N.I.

AU - Giudici, Michael

AU - Hawtin, Dan

AU - Praeger, Cheryl

PY - 2016/6/1

Y1 - 2016/6/1

N2 - © 2015, Springer Science+Business Media New York. We consider a code to be a subset of the vertex set of a Hamming graph. The set of (Formula presented.) -neighbours of a code is the set of vertices, not in the code, at distance (Formula presented.) from some codeword, but not distance less than (Formula presented.) from any codeword. A (Formula presented.) -neighbour transitive code is a code which admits a group (Formula presented.) of automorphisms which is transitive on the (Formula presented.) -neighbours, for (Formula presented.) , and transitive on the code itself. We give a classification of (Formula presented.) -neighbour transitive codes, with minimum distance (Formula presented.) , for which (Formula presented.) acts faithfully on the set of entries of the Hamming graph.

AB - © 2015, Springer Science+Business Media New York. We consider a code to be a subset of the vertex set of a Hamming graph. The set of (Formula presented.) -neighbours of a code is the set of vertices, not in the code, at distance (Formula presented.) from some codeword, but not distance less than (Formula presented.) from any codeword. A (Formula presented.) -neighbour transitive code is a code which admits a group (Formula presented.) of automorphisms which is transitive on the (Formula presented.) -neighbours, for (Formula presented.) , and transitive on the code itself. We give a classification of (Formula presented.) -neighbour transitive codes, with minimum distance (Formula presented.) , for which (Formula presented.) acts faithfully on the set of entries of the Hamming graph.

U2 - 10.1007/s10623-015-0069-3

DO - 10.1007/s10623-015-0069-3

M3 - Article

SN - 0925-1022

VL - 79

SP - 549

EP - 564

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 3

ER -

Entry-faithful 2-neighbour transitive codes

Abstract

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Group Actions: Combinatorics, Geometry and Computation

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