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Linear codes from arcs and quadrics

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Abstract

Using characterizations of ovals, KM-arcs and elliptic quadrics recently described in polar coordinates, we construct some families of LCD, self-orthogonal, three-weight and four-weight linear codes. We also demonstrate some applications to quantum codes.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their detailed comments, especially for pointing out the connection between the secants to a KM-arc and the weight enumerator of the linear code in Theorem 7. This allowed us to extend Theorems 8 and 9 in the revised version.

This work was supported by UAEU grant G00003490.

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  1. UAE University, PO Box 15551, Al Ain, UAE

    Kanat Abdukhalikov & Duy Ho

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  1. Kanat Abdukhalikov
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Correspondence to Duy Ho.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: Finite Geometries 2022”.

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Abdukhalikov, K., Ho, D. Linear codes from arcs and quadrics. Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01255-z

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  • DOI: https://doi.org/10.1007/s10623-023-01255-z

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