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Codes of length two correcting single errors of limited size

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Abstract

Linear codes of length 2 over the integers modulo some integer q that can correct single errors of limited size are considered. A code can be determined by a check pair of integers. For a given range of integers, − μ ≤ e ≤ λ, such a code can only exist for q sufficiently large. The main content of this note is to make this statement precise, that is, to determine “q sufficiently large” in terms of the integers − μ and λ.

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  1. Department of Informatics, University of Bergen, 5020, Bergen, Norway

    Torleiv Kløve

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  1. Torleiv Kløve
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Correspondence to Torleiv Kløve.

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This article is part of the Topical Collection on Special Issue: Mathematical Methods for Cryptography

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Kløve, T. Codes of length two correcting single errors of limited size. Cryptogr. Commun. 11, 549–555 (2019). https://doi.org/10.1007/s12095-018-0327-0

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  • DOI: https://doi.org/10.1007/s12095-018-0327-0

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