Author, as appears in the article.: Bras-Amoros, Maria; Duursma, Iwan; Hong, Euijin;

Department: Enginyeria Informàtica i Matemàtiques

URV's Author/s: Bras Amoros, Maria

Keywords: Punctured code Dual code Bounds Ag code 94b27 11t71

Abstract: Consider a complete flag {0} = C-0 < C-1 < center dot center dot center dot < C-n = F-n of one-point AG codes of length n over the finite field F. The codes are defined by evaluating functions with poles at a given point Q in points P-1, ... , P-n distinct from Q. A flag has the isometry-dual property if the given flag and the corresponding dual flag are the same up to isometry. For several curves, including the projective line, Hermitian curves, Suzuki curves, Ree curves, and the Klein curve over the field of eight elements, the maximal flag, obtained by evaluation in all rational points different from the point Q, is self-dual. More generally, we ask whether a flag obtained by evaluation in a proper subset of rational points is isometry-dual. In Geil et al. (2011) it is shown, for a curve of genus g, that a flag of one-point AG codes defined with a subset of n > 2g + 2 rational points is isometry-dual if and only if the last code C-n in the flag is defined with functions of pole order at most n + 2g - 1. Using a different approach, we extend this characterization to all subsets of size n >= 2g + 2. Moreover we show that this is best possible by giving examples of isometry-dual flags with n = 2g + 1 such that Cn is generated by functions of pole order at most n + 2g - 2. We also prove a necessary condition, formulated in terms of maximum sparse ideals of the Weierstrass semigroup of Q, under which a flag of punctured one-point AG codes inherits the isometry-dual property from the original unpunctured flag.

Thematic Areas: Theoretical computer science Mathematics, applied Matemática / probabilidade e estatística Engenharias iv Engenharias iii Discrete mathematics and combinatorics Computer science, theory & methods Computer science applications Ciência da computação Astronomia / física Applied mathematics

licence for use: https://creativecommons.org/licenses/by/3.0/es/

ISSN: 1573-7586

Author's mail: maria.bras@urv.cat

Author identifier: 0000-0002-3481-004X

Record's date: 2023-02-19

Papper version: info:eu-repo/semantics/acceptedVersion

Link to the original source: https://link.springer.com/article/10.1007%2Fs10623-020-00752-9

Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/

Papper original source: Designs Codes And Cryptography. 88 (8): 1617-1638

APA: Bras-Amoros, Maria; Duursma, Iwan; Hong, Euijin; (2020). Isometry-dual flags of AG codes. Designs Codes And Cryptography, 88(8), 1617-1638. DOI: 10.1007/s10623-020-00752-9

Article's DOI: 10.1007/s10623-020-00752-9

Entity: Universitat Rovira i Virgili

Journal publication year: 2020

Publication Type: Journal Publications