On the Weight Hierarchy of Codes Coming From Semigroups With Two Generators

• Type: Article in International Scientific Journal
• Date: 2014

Authors

delgado, m (Author) FCUP; farran, ji (Author) Other; garcia-sanchez, pa (Author) Other; llena, d (Author) Other

Journal

Title: IEEE Transactions on Information Theory

Vol. 60

Pages: 282-295

ISSN: 0018-9448

Publisher: IEEE

Indexing

ISI Web of Knowledge - 16 Citations

Scopus - 17 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-008-KDG

DOI: 10.1109/tit.2013.2285217

Abstract (EN): The weight hierarchy of one-point algebraic geometry codes can be estimated by means of the generalized order bounds, which are described in terms of a certain Weierstrass semi-group. The asymptotical behavior of such bounds for r >= 2 differs from that of the classical Feng-Rao distance (r = 1) by the so-called Feng-Rao numbers. This paper is addressed to compute the Feng-Rao numbers for numerical semigroups of embedding dimension two (with two generators), obtaining a closed simple formula for the general case by using numerical semigroup techniques. These involve the computation of the Apery set with respect to an integer of the semigroups under consideration. The formula obtained is applied to lower bounding the generalized Hamming weights, improving the bound given by Kirfel and Pellikaan in terms of the classical Feng-Rao distance. We also compare our bound with a modification of the Griesmer bound, improving this one in many cases.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14