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Efficient representation of binary nonlinear codes: constructions and minimum distance computation

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Abstract

A binary nonlinear code can be represented as a union of cosets of a binary linear subcode. In this paper, the complexity of some algorithms to obtain this representation is analyzed. Moreover, some properties and constructions of new codes from given ones in terms of this representation are described. Algorithms to compute the minimum distance of binary nonlinear codes, based on known algorithms for linear codes, are also established, along with an algorithm to decode such codes. All results are written in such a way that they can be easily transformed into algorithms, and the performance of these algorithms is evaluated.

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Acknowledgments

This work has been partially supported by the Spanish MICINN under Grants TIN2010-17358 and TIN2013-40524-P, and by the Catalan AGAUR under Grant 2014SGR-691. The material in this paper was presented in part at the Applications of Computer Algebra Conference, Málaga, Spain 2013 [22].

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  1. Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Mercè Villanueva, Fanxuan Zeng & Jaume Pujol

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  1. Mercè Villanueva
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  2. Fanxuan Zeng
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  3. Jaume Pujol
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Correspondence to Mercè Villanueva.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Computer Algebra in Coding Theory and Cryptography”.

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Villanueva, M., Zeng, F. & Pujol, J. Efficient representation of binary nonlinear codes: constructions and minimum distance computation. Des. Codes Cryptogr. 76, 3–21 (2015). https://doi.org/10.1007/s10623-014-0028-4

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  • DOI: https://doi.org/10.1007/s10623-014-0028-4

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