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The complete weight distribution of a subclass of optimal three-weight cyclic codes

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Abstract

The weight distribution of a code is usually investigated on the basis of Hamming weight, under which all the nonzero components of a codeword are regarded as identical. To describe the structure of nonbinary codes in more detail, each nonzero component should be distinguished from the other and this is done by means of the complete weight distribution. However, obtaining the complete weight distribution for nonbinary codes is an even harder problem than obtaining the ordinary weight distribution. Therefore, the complete weight distribution is unknown for most codes. The complete weight distributions of two classes of p-ary cyclic codes were recently reported by Heng and Yue (Cryptogr. Commun. 9, 323–343, 8). The purpose of this work is to present the complete weight distribution of a subclass of optimal three-weight cyclic codes over any finite field.

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Acknowledgments

The authors want to express their gratitude to the Associate Editor and the anonymous referees for their valuable suggestions.

Funding

The second author has received research support from CONACyT, México.

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Authors and Affiliations

  1. Dirección General de Cómputo y de Tecnologías de Información y Comunicación, Universidad Nacional Autónoma de México, 04510, Ciudad de México, Mexico

    Gerardo Vega

  2. Posgrado en Ciencia e Ingeniería de la Computación, Universidad Nacional Autónoma de México, 04510, Ciudad de México, Mexico

    Félix Hernández

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  1. Gerardo Vega
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  2. Félix Hernández
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Correspondence to Gerardo Vega.

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Vega, G., Hernández, F. The complete weight distribution of a subclass of optimal three-weight cyclic codes. Cryptogr. Commun. 15, 317–330 (2023). https://doi.org/10.1007/s12095-022-00601-7

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