ALGEBRAIC-GEOMETRIC CODES FROM CURVES OF SMALL GENUS.

A. M. Barg, G. L. Katsman, M. A. Tsfasman

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

The authors present a variant of Goppa's construction proposed by Yu. I. Manin, which uses curves of genus g with N//q points defined over F//q, to construct q-ary codes with parameters (N//q, k, d), where d plus k equals N//q minus g plus 1, and also a method for lengthening Goppe's codes by one symbol. Also presented without proof are some results on the number of F//q -points on curves of genus 1, 2, and 3. Q-ary codes are applied as outer codes for the construction of generalized concatenated codes. The parameters of the resulting codes are better than the parameters of the best known codes. All the 'best' values are listed in tables.

Original languageEnglish
Pages (from-to)34-38
Number of pages5
JournalProblems of information transmission
Volume23
Issue number1
Publication statusPublished - Jan 1987
Externally publishedYes

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