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Advances in Mathematics of Communications (AMC)
 

A $\mathbb Z$4-linear code of high minimum Lee distance derived from a hyperoval
Pages: 275 - 286, Volume 5, Issue 2, May 2011

doi:10.3934/amc.2011.5.275      Abstract        References        Full text (356.1K)           Related Articles

Michael Kiermaier - Institut für Mathematik, Universität Bayreuth, 95440 Bayreuth, Germany (email)
Johannes Zwanzger - Institut für Mathematik, Universität Bayreuth, 95440 Bayreuth, Germany (email)

1 I. Constantinescu and W. Heise, A metric for codes over residue class rings, Prob. Inform. Trans., 33 (1997), 208-213.       
2 T. Feulner, Canonization of linear codes over $\mathbbZ_4$, Adv. Math. Commun., 5 (2011), 245-266.
3 M. Greferath and S. E. Schmidt, Gray isometries for finite chain rings and a nonlinear ternary $(36,3$12$,15)$ code, IEEE Trans. Inform. Theory, 45 (1999), 2522-2524.       
4 M. Greferath and S. E. Schmidt, Finite-ring combinatorics and MacWilliams' equivalence theorem, J. Combin. Theory Ser. A, 92 (2000), 17-28.       
5 A. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The $\mathbbZ_4$-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40 (1994), 301-319.       
6 T. Honold and M. Kiermaier, Classification of maximal arcs in small projective Hjelmslev geometries, in "Proceedings of the Tenth International Workshop on Algebraic and Combinatorial Coding Theory (ACCT-10),'' (2006), 112-117.
7 T. Honold and I. Landjev, Linear codes over finite chain rings, Electr. J. Comb., 7 (2000), #R11.       
8 T. Honold and I. Landjev, On maximal arcs in projective Hjelmslev planes over chain rings of even characteristic, Finite Fields Appl., 11 (2005), 292-304.       
9 T. Honold and I. Landjev, Linear codes over finite chain rings and projective Hjelmslev geometries, in "Codes over Rings. Proceedings of the CIMPA Summer School Ankara, Turkey, August 2008'' (ed. P. Solé), World Scientific, (2009), 60-123.
10 T. Honold and A. A. Nechaev, Weighted modules and representations of codes, Prob. Inform. Trans., 35 (1999), 205-223.       
11 W. C. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes,'' Cambridge University Press, Cambridge, 2003.       
12 A. M. Kerdock, A class of low-rate non-linear binary codes, Inform. Control, 20 (1972), 182-187.       
13 S. Litsyn, E. Rains and N. Sloane, Table of nonlinear binary codes, http://www.eng.tau.ac.il/~litsyn/tableand/
14 A. A. Nechaev, Kerdock code in a cyclic form, Discrete Math. Appl., 1 (1991), 365-384.       
15 A. A. Nechaev and A. S. Kuzmin, Linearly presentable codes, in "Proceedings of the International Symposium on Information Theory and its Applications (ISITA) 1996,'' (1996), 31-34.
16 A. W. Nordstrom and J. P. Robinson, An optimum nonlinear code, Inform. Control, 11 (1967), 613-616.
17 F. P. Preparata, A class of optimum nonlinear double-error-correcting codes, Inform. Control, 13 (1968), 378-400.       
18 R. Raghavendran, Finite associative rings, Composito Math., 21 (1969), 195-229.       
19 H. C. A. van Tilborg, The smallest length of binary $7$-dimensional linear codes with prescribed minimum distance, Discrete Math., 33 (1981), 197-207.       
20 V. Zinoviev and S. Litsyn, On the general construction of codes shortening, Prob. Inform. Trans., 23 (1987), 111-116.       
21 J. Zwanzger, Linear codes over finite chain rings, http://www.mathe2.uni-bayreuth.de/20er/codedb/
22 J. Zwanzger, A heuristic algorithm for the construction of good linear codes, IEEE Trans. Inform. Theory, 54 (2008), 2388-2392.       

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