17 New Existences linear [n,3,d]19 Codes by Geometric Structure Method in PG(2,19)
نویسندگان
چکیده
منابع مشابه
New Ring-Linear Codes from Geometric Dualization
In the 1960s and 1970s the Nordstrom-Robinson-Code [30] and subsequently the infinite series of the Preparata[31], Kerdock[21], Delsarte-Goethals[6] and Goethals-Codes [7] were discovered. Apart from a few corner cases, all of these codes are non-linear binary block codes that have higher minimum distance than any known comparable (having equal size and length) linear binary code. We will call ...
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An infinite series of curves is constructed in order to show that all linear codes can be obtained from curves using Goppa's construction. If one imposes conditions on the degree of the divisor used, then we derive criteria for linear codes to be algebraic-geometric. In particular, we investigate the family of q-ary Hamming codes, and prove that only those with redundancy one or two, and the bi...
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It is well-known that the linear secret-sharing scheme (LSSS) can be constructed from linear error-correcting codes (Brickell [1], R.J. McEliece and D.V.Sarwate [2],Cramer, el.,[3]). The theory of linear codes from algebraic-geometric curves (algebraic-geometric (AG) codes or geometric Goppa code) has been well-developed since the work of V.Goppa and Tsfasman, Vladut, and Zink( see [17], [18] a...
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ژورنال
عنوان ژورنال: AL-Rafidain Journal of Computer Sciences and Mathematics
سال: 2020
ISSN: 2311-7990
DOI: 10.33899/csmj.2020.163503