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

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 asymptotic...

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Bibliographic Details
Published in:IEEE transactions on information theory 2015-09, Vol.61 (9), p.4938-4947
Main Authors: Farran, Jose I., Garcia-Sanchez, Pedro A.
Format: Article
Language:English
Subjects:
AG codes
Algebra
Apery sets
Arrays
Codes
Conductors
Cryptography
Erbium
Error correction codes
Feng-Rao numbers
generalized Hamming weights
Generators
Geometry
Hamming weight
inductive numerical semigroups
order bounds
Poles and towers
towers of function fields
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2456879