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Designs, Codes and Cryptography

Erschienen in:

29.11.2018

Additive perfect codes in Doob graphs

verfasst von: Minjia Shi, Daitao Huang, Denis S. Krotov

Erschienen in: Designs, Codes and Cryptography | Ausgabe 8/2019

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Abstract

The Doob graph D(m, n) is the Cartesian product of \(m>0\) copies of the Shrikhande graph and n copies of the complete graph of order 4. Naturally, D(m, n) can be represented as a Cayley graph on the additive group \((Z_4^2)^m \times (Z_2^2)^{n'} \times Z_4^{n''}\), where \(n'+n''=n\). A set of vertices of D(m, n) is called an additive code if it forms a subgroup of this group. We construct a 3-parameter class of additive perfect codes in Doob graphs and show that the known necessary conditions of the existence of additive 1-perfect codes in \(D(m,n'+n'')\) are sufficient. Additionally, two quasi-cyclic additive 1-perfect codes are constructed in \(D(155,0+31)\) and \(D(2667,0+127)\).

Vorheriger Artikel Cameron–Liebler sets of k-spaces in

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Titel: Additive perfect codes in Doob graphs
verfasst von: Minjia Shi
Daitao Huang
Denis S. Krotov
Publikationsdatum: 29.11.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 8/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0586-y

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