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Designs, Codes and Cryptography

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05.01.2019

Projective Reed–Muller type codes on higher dimensional scrolls

verfasst von: Cícero Carvalho, Xavier Ramírez-Mondragón, Victor G. L. Neumann, Horacio Tapia-Recillas

Erschienen in: Designs, Codes and Cryptography | Ausgabe 9/2019

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Abstract

In 1988 Lachaud introduced the class of projective Reed–Muller codes, defined by evaluating the space of homogeneous polynomials of a fixed degree d on the points of \(\mathbb {P}^n(\mathbb {F}_q)\). In this paper we evaluate the same space of polynomials on the points of a higher dimensional scroll, defined from a set of rational normal curves contained in complementary linear subspaces of a projective space. We determine a formula for the dimension of the codes, and the exact value of the dimension and the minimum distance in some special cases.

Vorheriger Artikel On (t, L)-fold perfect authentication and secrecy codes with arbitration

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Titel: Projective Reed–Muller type codes on higher dimensional scrolls
verfasst von: Cícero Carvalho
Xavier Ramírez-Mondragón
Victor G. L. Neumann
Horacio Tapia-Recillas
Publikationsdatum: 05.01.2019
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 9/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-00603-8

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