TY - JOUR

T1 - On automorphisms of linear codes over a prime field

AU - Avgustinovich, Sergey Vladimirovich

AU - Gorkunov, Evgeny Vladimirovich

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We discuss linearity of code automorphisms for codes ina space over a finite field. We introduce a concept of minimal supportsand minimal codewords, which in some cases are turned out useful toprove that an automorphism of a linear code is linear. Also we constructa graph on the set of minimal supports of a code as a vertex set. In thispaper for a linear code in a space over a prime field it is shown that allits autotopies fixing the zero vector are linear if and only if the graph ofminimal supports of the code does not contain any isolated vertices. Wealso characterize the autotopy group of a linear code over a prime field.

AB - We discuss linearity of code automorphisms for codes ina space over a finite field. We introduce a concept of minimal supportsand minimal codewords, which in some cases are turned out useful toprove that an automorphism of a linear code is linear. Also we constructa graph on the set of minimal supports of a code as a vertex set. In thispaper for a linear code in a space over a prime field it is shown that allits autotopies fixing the zero vector are linear if and only if the graph ofminimal supports of the code does not contain any isolated vertices. Wealso characterize the autotopy group of a linear code over a prime field.

KW - Code automorphism

KW - Finite field

KW - Graph of minimal supports

KW - Lin-early rigid code

KW - Linear automorphism

KW - Linear code

KW - Minimal codeword

KW - Prime field

UR - http://www.scopus.com/inward/record.url?scp=85021336640&partnerID=8YFLogxK

U2 - 10.17377/semi.2017.14.021

DO - 10.17377/semi.2017.14.021

M3 - Article

AN - SCOPUS:85021336640

VL - 14

SP - 210

EP - 217

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -