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The minimum weights of two-point AG codes on norm-trace curves

Title
The minimum weights of two-point AG codes on norm-trace curves
Authors
Kim, BoranLee, Yoonjin
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2018
Journal Title
FINITE FIELDS AND THEIR APPLICATIONS
ISSN
1071-5797JCR Link

1090-2465JCR Link
Citation
FINITE FIELDS AND THEIR APPLICATIONS vol. 53, pp. 113 - 139
Keywords
Algebraic geometry codesAG codesThe order boundMinimum weightsNorm-trace curves
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
We construct two-point algebraic geometry codes (AG codes) on algebraic curves over a finite field. We find the order-like bound on the minimum weights of these codes on algebraic curves, and we prove that this order-like bound is better than the Goppa bound. On norm-trace curves over the finite fields of characteristic 2, we explicitly determine the order like bounds for one-point AG codes and two-point AG codes. Consequently, it turns out that the order-like bound for two point AG codes on norm-trace curves is better than that of one-point codes on the same curves except for a few cases. (C) 2018 Elsevier Inc. All rights reserved.
DOI
10.1016/j.ffa.2018.06.005
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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