<abstract xmlns="http://www.w3.org/1999/xhtml">Binary codes created by doubling construction, including quasi-perfect ones with distance d = 4, are investigated. All [17·2r−6, 17·2r−6 − r, 4] quasi-perfect codes are classified. Weight spectrum of the codes dual to quasi-perfect ones with d = 4 is obtained. The automorphism group Aut(C) of codes obtained by doubling construction is studied. A subgroup of Aut(C) is described and it is proved that the subgroup coincides with Aut(C) if the starting matrix of doubling construction has an odd number of columns. (It happens for all quasi-perfect codes with d = 4 except for Hamming one.) The properness and t-properness for error detection of codes obtained by doubling construction are considered.</abstract>

Binary codes created by doubling construction, including quasi-perfect ones with distance d = 4, are investigated. All [17·2r−6, 17·2r−6 − r, 4] quasi-perfect codes are classified. Weight spectrum of the codes dual to quasi-perfect ones with d = 4 is obtained. The automorphism group Aut(C) of codes obtained by doubling construction is studied. A subgroup of Aut(C) is described and it is proved that the subgroup coincides with Aut(C) if the starting matrix of doubling construction has an odd number of columns. (It happens for all quasi-perfect codes with d = 4 except for Hamming one.) The properness and t-properness for error detection of codes obtained by doubling construction are considered.

New Results on Binary Codes Obtained by Doubling Construction

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"New Results on Binary Codes Obtained by Doubling Construction"}

Binary codes created by doubling construction, including quasi-perfect ones with distance d = 4, are investigated. All [17·2r−6, 17·2r−6 − r, 4] quasi-perfect...

New Results on Binary Codes Obtained by Doubling Construction

Published Online: May 26, 2018

Page range: 63 - 76

Received: Sep 30, 2017

Accepted: Dec 08, 2017

DOI: https://doi.org/10.2478/cait-2018-0021

Keywords
Linear binary codes, doubling construction, quasi-perfect codes, automorphism group of a code, proper and t-proper codes

© 2018 Alexander A. Davydov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

New Results on Binary Codes Obtained by Doubling Construction

Published Online: May 26, 2018

Page range: 63 - 76

Received: Sep 30, 2017

Accepted: Dec 08, 2017

DOI: https://doi.org/10.2478/cait-2018-0021

KeywordsLinear binary codes, doubling construction, quasi-perfect codes, automorphism group of a code, proper and t-proper codes

© 2018 Alexander A. Davydov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Linear binary codes, doubling construction, quasi-perfect codes, automorphism group of a code, proper and t-proper codes