Maximum intersection of linear codes and~codes~equivalent to~linear
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 4, pp. 5-15.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $q\geqslant 3$ for the size of the intersection of two different pseudolinear codes of the same size $M$. Bibliogr. 10.
Keywords: linear code, pseudolinear code, code intersection, isometry, isotopy, finite field.
Mots-clés : MDS-code, equivalent codes
@article{DA_2019_26_4_a0,
     author = {S. V. Avgustinovich and E. V. Gorkunov},
     title = {Maximum intersection of linear codes and~codes~equivalent to~linear},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {5--15},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2019_26_4_a0/}
}
TY  - JOUR
AU  - S. V. Avgustinovich
AU  - E. V. Gorkunov
TI  - Maximum intersection of linear codes and~codes~equivalent to~linear
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2019
SP  - 5
EP  - 15
VL  - 26
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2019_26_4_a0/
LA  - ru
ID  - DA_2019_26_4_a0
ER  - 
%0 Journal Article
%A S. V. Avgustinovich
%A E. V. Gorkunov
%T Maximum intersection of linear codes and~codes~equivalent to~linear
%J Diskretnyj analiz i issledovanie operacij
%D 2019
%P 5-15
%V 26
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2019_26_4_a0/
%G ru
%F DA_2019_26_4_a0
S. V. Avgustinovich; E. V. Gorkunov. Maximum intersection of linear codes and~codes~equivalent to~linear. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 4, pp. 5-15. http://geodesic.mathdoc.fr/item/DA_2019_26_4_a0/

[1] A. A. Markov, “On transformations without error propagation”, Selected Works, v. II, Theory of Algorithms and Constructive Mathematics. Mathematical Logic. Information Science and Related Topics, MTsNMO, M., 2003, 70–93 (Russian)

[2] E. Bar-Yahalom, T. Etzion, “Intersection of isomorphic linear codes”, J. Comb. Theory., Ser. A, 80:1 (1997), 247–256 | DOI | MR | Zbl

[3] T. Etzion, A. Vardy, “Perfect binary codes and tilings: problems and solutions”, SIAM J. Discrete Math., 11:2 (1998), 205–223 | DOI | MR | Zbl

[4] V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Probl. Inf. Transm., 48:1 (2012), 47–55 | DOI | MR | Zbl

[5] S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “Partitions of an n-cube into nonequivalent perfect codes”, Probl. Inf. Transm., 43:4 (2007), 310–315 | DOI | MR | Zbl

[6] A. V. Los', F. I. Solov'eva, “On partitions of the space $F_q^N$ into affine nonequivalent perfect $q$-ary codes”, Sib. Elektron. Mat. Izv., 7 (2010), 425–434 (Russian) | MR | Zbl

[7] F. J. MacWilliams, N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977 | MR | Zbl

[8] S. Frisch, “On the minimal distance between group tables”, Acta Sci. Math. (Szeged), 63 (1997), 341–351 | MR | Zbl

[9] D. S. Krotov, V. N. Potapov, P. V. Sokolova, “On reconstructing reducible $n$-ary quasigroups and switching subquasigroups”, Quasigr. Relat. Syst., 16 (2008), 55–67 | MR | Zbl

[10] V. N. Potapov, D. S. Krotov, “Asymptotics for the number of $n$-quasigroups of order $4$”, Sib. Math. J., 47:4 (2006), 720–731 | DOI | MR | Zbl