Ideals of Numerical Semigroups and Error-Correcting Codes

Identifier:  imarina:6012534

Handle: https://hdl.handle.net/20.500.11797/imarina6012534

Authors:  Miguel Serradilla-Merinero, Jose

Abstract:
Several results relating additive ideals of numerical semigroups and algebraic-geometry codes are presented. In particular, we deal with the set of non-redundant parity-checks, the code length, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometry codes from the perspective of the related Weierstrass semigroups. These results are related to cryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, network coding, and ramp secret sharing schemes.