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Edoukou, Frédéric A. B.; Ling, San; Xing, Chaoping

Structure of functional codes defined on non-degenerate Hermitian varieties. (English) Zbl 1230.94012

J. Comb. Theory, Ser. A 118, No. 8, 2436-2444 (2011).
Summary: We study the functional codes of order \(h\) defined by G. Lachaud on a non-degenerate Hermitian variety, by exhibiting a result on divisibility for all the weights of such codes. In the case where the functional code is defined by evaluating quadratic functions on the non-degenerate Hermitian surface, we list the first five weights, describe the geometrical structure of the corresponding quadrics and give a positive answer to a conjecture formulated on this question by F. A. B. Edoukou [J. Théor. Nombres Bordx. 21, No. 1, 131–143 (2009; Zbl 1183.94060)]. The paper ends with two conjectures. The first is about the divisibility of the weights in the functional codes. The second is about the minimum distance and the distribution of the codewords of the first \(2h+1\) weights.

Cited in 1 Review
Cited in 6 Documents

MSC:

94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory
14G50 Applications to coding theory and cryptography of arithmetic geometry

Keywords:

divisor of a code; functional codes; Hermitian surface; Hermitian variety; weights of codes

Citations:

Zbl 1183.94060
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Full Text: DOI

References:

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