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Designs, Codes and Cryptography

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28.03.2019

On the weight distribution of second order Reed–Muller codes and their relatives

verfasst von: Shuxing Li

Erschienen in: Designs, Codes and Cryptography | Ausgabe 10/2019

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Abstract

The weight distribution of second order q-ary Reed–Muller codes have been determined by Sloane and Berlekamp (IEEE Trans. Inform. Theory, vol. IT-16, 1970) for \(q=2\) and by McEliece (JPL Space Progr Summ 3:28–33, 1969) for general prime power q. Unfortunately, there were some mistakes in the computation of the latter one. This paper aims to provide a precise account for the weight distribution of second order q-ary Reed–Muller codes. In addition, the weight distributions of second order q-ary homogeneous Reed–Muller codes and second order q-ary projective Reed–Muller codes are also determined.

Vorheriger Artikel Construction and enumeration for self-dual cyclic codes over of oddly even length

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Titel: On the weight distribution of second order Reed–Muller codes and their relatives
verfasst von: Shuxing Li
Publikationsdatum: 28.03.2019
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 10/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-019-00630-z

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On the weight distribution of second order Reed–Muller codes and their relatives

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