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Journal of Applied and Industrial Mathematics, 2019, 13:4, 600-605
Volume 26, No 4, 2019, P. 5-15
UDC 519.725
S. V. Avgustinovich and E. V. Gorkunov
Maximum intersection of linear codes and codes equivalent to linear
Abstract:
We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an isometric transformation of the space. We derive an upper bound $(q - 2)M/q$ attainable for $q \ge 3$ for the size of the intersection of two different pseudolinear codes of the same size $M$.
Bibliogr. 10.
Keywords: linear code, pseudolinear code, MDS-code, code intersection, equivalent codes, isometry, isotopy, finite field.
DOI: 10.33048/daio.2019.26.669
Sergey V. Avgustinovich 1,2
Evgeny V. Gorkunov 1,2
1. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: avgust@math.nsc.ru, gorkunov@math.nsc.ru
Received July 23, 2019
Revised August 27, 2019
Accepted August 28, 2019
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