Symmetric matrices and codes correcting rank errors beyond the ⌊(d-1)/2⌋

Discrete Applied Mathematics

Volumn 154, Issue 2, 2006, Pages 305-312

  Gabidulin, Ernst M ^a   Pilipchuk, Nina I ^a  

^a MOSCOW INSTITUTE OF PHYSICS AND TECHNOLOGY   (Russian Federation)

Author keywords

Correcting errors beyond the one half distance bound; Matrix rank linear codes; Self orthogonal bases; Vector rank linear codes

Indexed keywords

CODES (SYMBOLS); ERROR ANALYSIS; VECTORS;

CORRECTING ERRORS BEYOND THE HALF-DISTANCE; MATRIX RANK LINEAR CODES; SELF-ORTHOGONAL BASES; VECTOR RANK LINEAR CODES;

MATRIX ALGEBRA;

EID: 29244469097     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2005.03.012     Document Type: Conference Paper

References (8)

1. E.M. Gabidulin Theory of codes with maximum rank distance Problems of Information Transmission 21 1 1985 3 14
2. E.M. Gabidulin, A fast matrix decoding algorithm for rank-error- correcting codes, In: G. Cohen, S. Litsyn, A. Lobstein, G. Zemor (Eds.), Algebraic Coding, Lecture Notes in Computer Science, vol. 573, Springer, Berlin, 1992, pp. 126-132.
3. E.M. Gabidulin, M. Bossert, P. Lusina, Space-time codes based on rank codes, Proceedings of the 2000 IEEE International Symposium on Information Theory, Sorrento, Italy, 25-30 June, 2000, p. 283.
4. E.M. Gabidulin, A.V. Paramonov, O.V. Tretjakov, Ideals over a non-commutative ring and their application in cryptology, Lecture Notes in Computer Science, Advances in Cryptology, Proceedings of EUROCRYPT'91, vol. 547, Brighton, UK, April 1991, pp. 482-489.
5. E.M. Gabidulin, and N.I. Pilipchuk Symmetric rank codes Problems of Information Transmission 40 2 2004 3 18
6. F.J. MacWilliams, and N.J.A. Sloane The Theory of Error Correcting Codes eighth ed. 1993 North Holland Press Amsterdam
7. R.M. Roth Maximum-rank array codes and their application to crisscross error correction IEEE Trans. Inform. Theory 37 2 1991 328 336
8. G. Seroussi, and A. Lempel Factorization of symmetric matrices and trace-orthogonal bases in finite fields SIAM J. Comput. 9 4 1980 758 767