Abstract
We show that there are long self-dual q-ary quasi-cyclic codes above the Gilbert-Varshamov bound for odd q. We use Hughes’s (u + v|u - v) construction.
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References
J.H. Conway, V. Pless & N.J.A. Sloane Self-dual codes over GF(3) and GF(4) of length not exceeding 16, IEEE Trans. Inform. Theory 25 (1979), 312–322
G. Hughes Codes and arrays from cocycles Ph.D. thesis, Royal Melbourne Institute of Technology, 2000
G. Hughes Constacyclic codes cocycles and a u+ v u-v construction IEEE Trans. Inform. Theory 46 (2000), 674–680
T. Kasami A Gilbert-Varshamov bound for quasi-cyclic codes of rate 1/2, IEEE Trans. Inform. Theory 20 (1974), 679
S. Ling & P. Solé On the algebraic structure of quasi-cyclic codes I: finite fields IEEE Trans. Inform. Theory 47 (2001), 2751–2760
S. Ling & P. Solé Good self-dual quasi-cyclic codes exist IEEE Trans. Inform. Theory 49 (2003), 1052–1053
F.J. MacWilliams, N.J.A. Sloane & J.G. Thompson Good self-dual codes exist Discrete Math 3 (1972), 153–162
V. Pless & J.N. Pierce Self-dual codes over GF(q) satisfy a modified VarshamovGilbert bound Information and Control 23 (1973), 35–40
E.M. Rains & N.J.A. Sloane Self-dual codes in Handbook of Coding Theory Vol. II, V.S. Pless & W.C. Huffman eds., Elsevier Science, Amsterdam, 1998, pp. 177–294
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Ling, S., Solé, P. (2004). Good Self-Dual Quasi-Cyclic Codes over Fq, q Odd. In: Feng, K., Niederreiter, H., Xing, C. (eds) Coding, Cryptography and Combinatorics. Progress in Computer Science and Applied Logic, vol 23. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7865-4_14
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DOI: https://doi.org/10.1007/978-3-0348-7865-4_14
Publisher Name: Birkhäuser, Basel
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