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This article is cited in 1 scientific paper (total in 1 paper)
Discrete mathematics and mathematical cybernetics
On automorphisms of linear codes over a prime field
S. V. Avgustinovichab, E. V. Gorkunovab a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090 Novosibirsk, Russia
b Novosibirsk State University, ul. Pirogova, 2, 630090 Novosibirsk, Russia
Abstract:
We discuss linearity of code automorphisms for codes in a space over a finite field. We introduce a concept of minimal supports and minimal codewords, which in some cases are turned out useful to prove that an automorphism of a linear code is linear. Also we construct a graph on the set of minimal supports of a code as a vertex set. In this paper for a linear code in a space over a prime field it is shown that all its autotopies fixing the zero vector are linear if and only if the graph of minimal supports of the code does not contain any isolated vertices. We also characterize the autotopy group of a linear code over a prime field.
Keywords:
linear code, code automorphism, linear automorphism, linearly rigid code, minimal codeword, graph of minimal supports, finite
field, prime field.
Received December 7, 2016, published March 14, 2017
Citation:
S. V. Avgustinovich, E. V. Gorkunov, “On automorphisms of linear codes over a prime field”, Sib. Èlektron. Mat. Izv., 14 (2017), 210–217
Linking options:
https://www.mathnet.ru/eng/semr780 https://www.mathnet.ru/eng/semr/v14/p210
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