2017/02/27 by José Ignacio Farrán, Farrán, J. I., Pedro A. García-Sánchez +3
Computer Science · Mathematics · #11T71 #11Y55 #20M14 #Coding theory and cryptography #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1702.08225
openalex publication_date 2017/02/27 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a lower bound for the second Hamming weight for one point AG codes. In particular, we can obtain the second Feng-Rao distance for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, we compute the second Feng-Rao number, and provide some examples and comparisons with previous results on this topic. These calculations rely on Apéry sets, and thus several results concerning Apéry sets of Arf semigroups are presented.