Constructing codes from algebraic curves

Date

1999-11-01

Author

Özbudak, Ferruh

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We discuss some recent constructions of codes from algebraic curves due to Xing, Niederreiter, and Lam, and we investigate their relations with Goppa's algebraic-geometric codes.

Subject Keywords

Algebraic curves, Algebraic function fields, AG codes, Geometric Goppa codes

URI

https://hdl.handle.net/11511/42815

Journal

IEEE TRANSACTIONS ON INFORMATION THEORY

DOI

https://doi.org/10.1109/18.796391

Collections

Department of Mathematics, Article

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Constructing linear unequal error protection codes from algebraic curves Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2003-06-01) We show that the concept of "generalized algebraic geometry codes" which was recently introduced by Xing, Niederreiter, and Lam gives a natural framework for constructing linear unequal error protection codes.
Classification of function fields with class number three BİLHAN, Mehpare; Buyruk, Dilek; Özbudak, Ferruh (2015-11-01) We give the full list of all algebraic function fields over a finite field with class number three up to isomorphism. Our list consists of explicit equations of algebraic function fields which are mutually non-isomorphic over the full constant field.
Construction of Some Codes Suitable for Both Side Channel and Fault Injection Attacks Carlet, Claude; GÜNERİ, CEM; Mesnager, Sihem; Özbudak, Ferruh (2018-12-30) Using algebraic curves over finite fields, we construct some codes suitable for being used in the countermeasure called Direct Sum Masking which allows, when properly implemented, to protect the whole cryptographic block cipher algorithm against side channel attacks and fault injection attacks, simultaneously. These codes address a problem which has its own interest in coding theory.
Structure and performance of generalized quasi-cyclic codes Guneri, Cem; Özbudak, Ferruh; Ozkaya, Buket; Sacikara, Elif; SEPASDAR, Zahra; SOLÉ, Patrick (2017-09-01) Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder Theorem yields a decomposition of GQC codes into a sum of concatenated codes. This decomposition leads to a trace formula, a minimum distance bound, and to a criteria for the GQC code to be self-dual or to be linear complementary dual (LCD). Explicit long GQC codes that ar...
On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields Özbudak, Ferruh; YAYLA, OĞUZ (2014-09-18) We determined the number of rational points of fibre products of two Kummer covers over a rational point of the projective line in a recent work of F. Ozbudak and B. G. Temur (Des Codes Cryptogr 70(3): 385-404, 2014), where we also constructed explicit examples, including a record and two new entries for the current Table of Curves with Many Points (manYPoints: Table of curves with many points. http://www.manypoints.org (2014). Accessed 30 Sep 2014). Using the methods given in Ozbudak and Gulmez Temur (Des ...

Citation Formats

F. Özbudak, “Constructing codes from algebraic curves,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 2502–2505, 1999, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42815.