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Binary Two-Error-Correcting Codes are Better than Quaternary

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

Codes over large fields can be used to construct codes over subfields. Such constructions of covering and error-correcting codes are discussed. In particular, packings and coverings with spheres of radius two are considered. A new construction of binary two-error-correcting codes from quaternary two-error-correcting codes is presented. This construction maintains the density, showing that such binary codes are at least as good as quaternary codes. The same construction is used to arrive at a similar conclusion for covering codes.

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  1. Department of Electrical and Communications Engineering, Helsinki University of Technology, P.O. Box 3000, 02015, HUT, Finland

    Patric R. J. Östergård

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  1. Patric R. J. Östergård
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Correspondence to Patric R. J. Östergård.

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Keywords: Bounds on codes, Covering code, Error-correcting code, Finite field.

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Östergård, P. Binary Two-Error-Correcting Codes are Better than Quaternary. AAECC 14, 89–96 (2003). https://doi.org/10.1007/s00200-003-0128-2

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  • DOI: https://doi.org/10.1007/s00200-003-0128-2

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