On polyalphabetic block codes

V. Sidorenko; G. Schmidt; E. Gabidulin; M. Bossert; V. Afanassiev

doi:10.1109/ITW.2005.1531889

On polyalphabetic block codes

V. Sidorenko, G. Schmidt, E. Gabidulin, M. Bossert, V. Afanassiev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

11 Scopus citations

Abstract

A polyalphabetic (or mixed) block code is a set of codewords of finite length, where every symbol of a codeword belongs to its own alphabet. In contrast to previous publications we consider a general case, where we do not assume any algebraic structure of the alphabets and the codes. Upper and lower bounds on the cardinality of a polyalphabetic code with given Hamming distance are obtained. Some constructions of polyalphabetic codes are suggested based on known codes. Encoding and decoding of the polyalphabetic codes, obtained in this way, can be done using encoding and decoding algorithms for the mother code. Using this constructions, codes are obtained, that reach the upper Singleton type bound.

Original language	English
Title of host publication	Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005
Pages	207-210
Number of pages	4
DOIs	https://doi.org/10.1109/ITW.2005.1531889
State	Published - 2005
Externally published	Yes
Event	IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005 - Rotorua, New Zealand Duration: 29 Aug 2005 → 1 Sep 2005

Publication series

Name	Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005

Conference

Conference	IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005
Country/Territory	New Zealand
City	Rotorua
Period	29/08/05 → 1/09/05

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10.1109/ITW.2005.1531889

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Sidorenko, V., Schmidt, G., Gabidulin, E., Bossert, M., & Afanassiev, V. (2005). On polyalphabetic block codes. In Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005 (pp. 207-210). Article 1531889 (Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005). https://doi.org/10.1109/ITW.2005.1531889

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title = "On polyalphabetic block codes",

abstract = "A polyalphabetic (or mixed) block code is a set of codewords of finite length, where every symbol of a codeword belongs to its own alphabet. In contrast to previous publications we consider a general case, where we do not assume any algebraic structure of the alphabets and the codes. Upper and lower bounds on the cardinality of a polyalphabetic code with given Hamming distance are obtained. Some constructions of polyalphabetic codes are suggested based on known codes. Encoding and decoding of the polyalphabetic codes, obtained in this way, can be done using encoding and decoding algorithms for the mother code. Using this constructions, codes are obtained, that reach the upper Singleton type bound.",

author = "V. Sidorenko and G. Schmidt and E. Gabidulin and M. Bossert and V. Afanassiev",

year = "2005",

doi = "10.1109/ITW.2005.1531889",

language = "English",

isbn = "078039481X",

series = "Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005",

pages = "207--210",

booktitle = "Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005",

note = "IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005 ; Conference date: 29-08-2005 Through 01-09-2005",

}

Sidorenko, V, Schmidt, G, Gabidulin, E, Bossert, M & Afanassiev, V 2005, On polyalphabetic block codes. in Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005., 1531889, Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005, pp. 207-210, IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005, Rotorua, New Zealand, 29/08/05. https://doi.org/10.1109/ITW.2005.1531889

On polyalphabetic block codes. / Sidorenko, V.; Schmidt, G.; Gabidulin, E. et al.
Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005. 2005. p. 207-210 1531889 (Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - A polyalphabetic (or mixed) block code is a set of codewords of finite length, where every symbol of a codeword belongs to its own alphabet. In contrast to previous publications we consider a general case, where we do not assume any algebraic structure of the alphabets and the codes. Upper and lower bounds on the cardinality of a polyalphabetic code with given Hamming distance are obtained. Some constructions of polyalphabetic codes are suggested based on known codes. Encoding and decoding of the polyalphabetic codes, obtained in this way, can be done using encoding and decoding algorithms for the mother code. Using this constructions, codes are obtained, that reach the upper Singleton type bound.

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On polyalphabetic block codes

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