Upper bounds for the size of binary codes

Alinaghipour Fatemeh; Ahmadi Bahman

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ALINAGHIPOUR, Fatemeh, AHMADI, Bahman. Upper bounds for the size of binary codes. In: Conference on Applied and Industrial Mathematics: CAIM 2017, 14-17 septembrie 2017, Iași. Chișinău: Casa Editorial-Poligrafică „Bons Offices”, 2017, Ediţia 25, p. 58. ISBN 978-9975-76-247-2.

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Conference on Applied and Industrial Mathematics
Ediţia 25, 2017

Conferința "Conference on Applied and Industrial Mathematics"
Iași, Romania, 14-17 septembrie 2017

Upper bounds for the size of binary codes

Pag. 58-58

Alinaghipour Fatemeh, Ahmadi Bahman

Shiraz University

Disponibil în IBN: 10 ianuarie 2024

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Any subset C of the group Znq is called a q-ary code of length n. For any element c 2 C, the weight of c, i.e. the number of non-zero entries of c, is denoted by wt(c). The Hamming distance of any two elements c1; c2 2 C is de ned to be dist(c1; c2) = wt(c1-c2). Also the minimum hamming distance of a code C is de ned to be the largest integer d such that for any c1; c2 2 C, we have dist(c1; c2) d. The maximum size of any q-ary code of length n with minimum Hamming distance d is denoted by Aq(n; d). It this talk, we will provide an overview of a technique which employs representation theory of nite groups as well as some graph theoretical techniques to obtain some upper bounds for A2(n; d).

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