Advances in Mathematics of Communications (AMC)

Canonization of linear codes over $\mathbb Z$4
Pages: 245 - 266, Volume 5, Issue 2, May 2011

doi:10.3934/amc.2011.5.245      Abstract        References        Full text (509.6K)           Related Articles

Thomas Feulner - Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany (email)

1 A. Betten, M. Braun, H. Fripertinger, A. Kerber, A. Kohnert and A. Wassermann, "Error-Correcting Linear Codes, Classification by Isometry and Applications,'' Springer, Berlin, 2006.       
2 T. Feulner, The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes, Adv. Math. Commun., 3 (2009), 363-383.       
3 A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. SolĂ©, The $\mathbbZ_4$-linearity of Kerdock, Preperata, Goethals and related codes, IEEE Trans. Inform. Theory, 40 (1994), 301-319.       
4 T. Honold and I. Landjev, Linear codes over finite chain rings, Electron. J. Comb., 7 (1998), 116-126.       
5 W. C. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes,'' Cambridge University Press, Cambridge, 2003.       
6 M. Kiermaier and J. Zwanzger, A $\mathbbZ_4$-linear code of high minimum Lee distance derived from a hyperoval, Adv. Math. Commun., 5 (2011), 275-286.
7 R. Laue, Constructing objects up to isomorphism, simple 9-designs with small parameters, in "Algebraic Combinatorics and Applications,'' Springer, (2001), 232-260.       
8 J. S. Leon, Computing automorphism groups of error-correcting codes, IEEE Trans. Inform. Theory, 28 (1982), 496-511.       
9 B. D. McKay, Isomorph-free exhaustive generation, J. Algorithms, 26 (1998), 306-324.       
10 A. A. Nechaev, Kerdock's code in cyclic form, Diskret. Mat., 1 (1989), 123-139.       
11 E. Petrank and R. M. Roth, Is code equivalence easy to decide?, IEEE Trans. Inform. Theory, 43 (1997), 1602-1604.       
12 C. C. Sims, Computation with permutation groups, in "Proceedings of the Second ACM Symposium on Symbolic and Algebraic Manipulation, SYMSAC '71,'' (1971), 23-28.

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