Algorithms for computing parameters of graph-based extensions of BCH codes

Bača, 2004, Antimagic labelings of generalized Petersen graphs that are plane, Ars Combin., 73, 115 Bača, 2003, On d-antimagic labelings of type (1,1,1) for prisms, J. Combin. Math. Combin. Comput., 44, 199 Bača, 2002, Vertex-magic total labelings of generalized Petersen graphs, Int. J. Comput. Math., 79, 1259, 10.1080/00207160214650 Bierbrauer, 1997, Extending and lengthening BCH codes, Finite Fields Appl., 3, 314, 10.1006/ffta.1997.0188 Bierbrauer, 1999, New codes via the lengthening of BCH codes with UEP codes, Finite Fields Appl., 5, 345, 10.1006/ffta.1999.0245 Chen, 1999, On minimum Lee weights of Hensel lifts of some binary BCH codes, IEEE Trans. Inform. Theory, 45, 2157, 10.1109/18.782167 Cormen, 2001 de Andrade, 1999, Construction and decoding of BCH codes over finite commutative rings, Linear Algebra Appl., 286, 69, 10.1016/S0024-3795(98)10163-5 Downey, 1999, Parameterized Complexity, 10.1007/978-1-4612-0515-9 Downey, 2001, The parametrized complexity of some fundamental problems in coding theory, SIAM J. Comput., 29, 545, 10.1137/S0097539797323571 Gallian, 2005, Graph labeling, Electronic J. Combinatorics, Dynamic Survey, DS6 Goodrich, 2001 Hernquist, 1999, Finding short and light codewords in BCH codes, IEEE Trans. Inform. Theory, 45, 255, 10.1109/18.746802 J. Holub, C.S. Iliopoulos, B. Melichar, L. Mouchard, Distributed string matching using finite automata, in: Combinatorial Algorithms, AWOCA 99, Perth, pp.114–127 Iliopoulos, 1985, Computing in general Abelian groups is hard, Theoret. Comput. Sci., 41, 81, 10.1016/0304-3975(85)90061-1 Interlando, 1997, On the decoding of Reed–Solomon and BCH codes over integer residue rings, IEEE Trans. Inform. Theory, 43, 1013, 10.1109/18.568713 Kelarev, 2002 Kelarev, 2003 A.V. Kelarev, Minimum distances and information rates for matrix extensions of BCH codes, in: The 3rd Workshop on the Internet, Telecommunications and Signal Processing, WITSP 2004, Adelaide, 20–22 December 2004, pp.1–6 Kelarev, 2006, A polynomial algorithm for codes based on directed graphs, vol. 51, 87 Kelarev, 2001, Information rates and weights of codes in structural matrix rings, vol. 2227, 151 Kelarev, 2001, Error-correcting codes as ideals in group rings, Abelian Groups, Rings, and Modules, 273, 11, 10.1090/conm/273/04419 Lidl, 1994 Lidl, 1997 Lin, 2001, Vertex magic total labelings of complete graphs, Bull. Inst. Combin. Appl., 33, 68 Lin, 2004, On d-antimagic labelings of prisms, Ars Combin., 72, 65 McHugh, 1990 McKay, 1979, Transitive graphs with fewer than twenty vertices, Math. Comp., 33, 1101, 10.1090/S0025-5718-1979-0528064-2 Miller, 2005, Exclusive sum labeling of graphs, J. Combin. Math. Combin. Comput., 55, 137 Miller, 2003, Distance magic labelings of graphs, Australas. J. Combin., 28, 305 Moffat, 2002 Pieprzyk, 2003 Pless, 1998 Smyth, 2003 Stallings, 2002 Street, 1977 Slamin, 2002, Edge-magic total labelings of wheels, fans and friendship graphs, Bull. Inst. Combin. Appl., 35, 89 Sugeng, 2005, Super (a,d)-vertex-antimagic total labelings, J. Combin. Math. Combin. Comput., 55, 91 Sugeng, 2005, Relationship between adjacency matrices and super (a,d)-edge-antimagic-total labeling of graphs, J. Combin. Math. Combin. Comput., 55, 71 Sugeng, 2005, (a,d)-edge-antimagic total labelings of caterpillars, vol. 3330, 169 Tuga, 2005, Exclusive sum labelings of trees, J. Combin. Math. Combin. Comput., 55, 109 Tuga, 2005, Δ-optimum exclusive sum labeling of certain graphs with radius one, vol. 3330, 216 van der Geer, 1994, On generalized Hamming weights of BCH codes, IEEE Trans. Inform. Theory, 40, 543, 10.1109/18.312183