Geodesic
On automorphisms of linear codes over a prime field
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 210-217

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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, linear automorphism, linearly rigid code, graph of minimal supports, finite field, prime field.
Mots-clés : code automorphism, minimal codeword 
@article{SEMR_2017_14_a70,
     author = {S. V. Avgustinovich and E. V. Gorkunov},
     title = {On automorphisms of linear codes over a prime field},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {210--217},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a70/}
}
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S. V. Avgustinovich; E. V. Gorkunov. On automorphisms of linear codes over a prime field. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 210-217. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a70/