On the generalized Feng-Rao numbers of numerical semigroups generated by intervals

DOI10.1090/S0025-5718-2013-02673-7zbMath1282.11163arXiv1105.4833MaRDI QIDQ2840632

Manuel Delgado, David Llena, José I. Farrán, Pedro A. García Sánchez

Publication date: 23 July 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.4833

zbMATH Keywords

weight hierarchynumerical semigroupsorder boundsAG codesFeng-Rao numbersGoppa-like bounds

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Commutative semigroups (20M14) Sequences and sets (11B99) Calculation of integer sequences (11Y55)

Related Items (3)

The second Feng-Rao number for codes coming from telescopic semigroups ⋮ On the second Feng-Rao distance of algebraic geometry codes related to Arf semigroups ⋮ On atomic density of numerical semigroup algebras

Uses Software

• numericalsgps

Cites Work

• Unnamed Item
• The weight distribution of irreducible cyclic codes with block lengths \(n_1 ((q^\ell-1)/N)\)
• Goppa-like bounds for the generalized Feng-Rao distances.
• Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models
• On the parameters of algebraic-geometry codes related to Arf semigroups
• The catenary and tame degree of numerical monoids
• Generalized Hamming weights for linear codes
• Decoding algebraic-geometric codes up to the designed minimum distance
• Generalized Hamming weights of q-ary Reed-Muller codes
• The minimum distance of codes in an array coming from telescopic semigroups
• The Weight Hierarchy of Hermitian Codes

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