In 1990 Cooper (Comm., Cont. and Sign. Proc. 281–286, 1990; Electronic Letters 27(22):2090–2091, 1991; Transactions of the Tenth Army Conference on AppliedMathematics and Computing (1992), vol. 93, U.S. Army, pp. 1–11, 1993) suggested to use Gröbner basis computations in order to deduce error locator polynomials of cyclic codes. The aim of this tutorial is to show, with illuminating examples, how Cooper’s approach has been refined (Caboara in Appl. Algebra Engrg. Comm. Comput. 13(3): 209–232, 2002; Chen et al. in IEEE Trans. on Inf. Th. 40:1661–1663, 1994a; Contemp. Math., vol. 168, Amer. Math. Soc., Providence, pp. 15–22, 1994b; IEEE Trans. on Inf. Th. 40(5):1654–1661, 1994c; Loustaunau and York in AAECC 8(6):469–483, 1997), up to give both an online decoder (Augot et al. in Proc. of ISIT 2003, pp. 362–362, 2003; Proc. of ISIT 2007, pp. 2646–2650, 2007) and general error locator polynomials (Orsini and Sala in J. Pure Appl. Algebra 200:191– 226, 2005; IEEE Trans. on Inf. Th. 53:1095–1107, 2007; Mora et al. in BCRI preprint, www.bcri.ucc.ie 43, UCC, Cork, Ireland, 2006)
Decoding Cyclic Codes: the Cooper Phylosophy
MORA, FERDINANDO;
2009-01-01
Abstract
In 1990 Cooper (Comm., Cont. and Sign. Proc. 281–286, 1990; Electronic Letters 27(22):2090–2091, 1991; Transactions of the Tenth Army Conference on AppliedMathematics and Computing (1992), vol. 93, U.S. Army, pp. 1–11, 1993) suggested to use Gröbner basis computations in order to deduce error locator polynomials of cyclic codes. The aim of this tutorial is to show, with illuminating examples, how Cooper’s approach has been refined (Caboara in Appl. Algebra Engrg. Comm. Comput. 13(3): 209–232, 2002; Chen et al. in IEEE Trans. on Inf. Th. 40:1661–1663, 1994a; Contemp. Math., vol. 168, Amer. Math. Soc., Providence, pp. 15–22, 1994b; IEEE Trans. on Inf. Th. 40(5):1654–1661, 1994c; Loustaunau and York in AAECC 8(6):469–483, 1997), up to give both an online decoder (Augot et al. in Proc. of ISIT 2003, pp. 362–362, 2003; Proc. of ISIT 2007, pp. 2646–2650, 2007) and general error locator polynomials (Orsini and Sala in J. Pure Appl. Algebra 200:191– 226, 2005; IEEE Trans. on Inf. Th. 53:1095–1107, 2007; Mora et al. in BCRI preprint, www.bcri.ucc.ie 43, UCC, Cork, Ireland, 2006)
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