The Second Feng-Rao Number for Codes Coming From Inductive Semigroups

Author

Farran, Jose I. ; Garcia-Sanchez, Pedro A.

Author_Institution

Dept. de Mat. Aplic., Univ. de Valladolid, Valladolid, Spain

Volume

61

Issue

9

fYear

2015

fDate

Sept. 2015

Firstpage

4938

Lastpage

4947

Abstract

The second Feng-Rao number of every inductive numerical semigroup is explicitly computed. This number determines the asymptotical behavior of the order bound for the second Hamming weight of one-point algebraic geometry codes. In particular, this result is applied for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, some properties of inductive numerical semigroups are studied, the involved Apéry sets are computed in a recursive way, and some tests to check whether given numerical semigroups are inductive or not are provided.

Keywords

algebraic geometric codes; group theory; number theory; numerical analysis; set theory; Apéry sets; Weierstrass semigroups; asymptotical order bound behavior; inductive numerical semigroups; one-point algebraic geometry codes; second Feng-Rao number; second Hamming weight; Arrays; Conductors; Erbium; Error correction codes; Generators; Hamming weight; Poles and towers; AG codes; Ap??ry sets; Apery sets; Feng-Rao numbers; generalized Hamming weights; inductive numerical semigroups; order bounds; towers of function fields;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2015.2456879

Filename

7159076