D. M. Gordon. Minimal permutation sets for decoding the binary Golay codes. IEEE Trans. Inform. Theory, 28:541--543, 1982. Home/Search Document Not in Database Summary Related Articles Check |
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Some Recent Results in Permutation Decoding - Key (Correct)
....t. Then the information symbols in y are correct if and only if the weight of the syndrome Hy of y is t. 5 31 Minimum size for a PD set Counting shows that there is a minimum size a PD set can have; most the sets known have size larger than this minimum. The following is due to Gordon [5], using a result of Schonheim [11] Result 2 If is a PD set for a t error correcting [n, k, d] q code C, and r = n k, then . Proof in Hu#man [6] Example: The binary extended Golay code, parameters [24, 12, 8] has n = 24, r = 12 and t = 3, so 24 23 ....
....t error correcting [n, k, d] q code C, and r = n k, then . Proof in Hu#man [6] Example: The binary extended Golay code, parameters [24, 12, 8] has n = 24, r = 12 and t = 3, so 24 23 11 22 10 = 14 and PD sets of this size has been found (see Gordon [5] and Wolfmann [12] 6 31 Magma results Some computational examples using Magma [3] 1. for C the [28, 21, 4] 2 code of the hermitian unital 2 (28,4,1) has 4; Aut(C) is Sp 6 (2) and a PD set of four elements can be found; 2. C # , for C as above, is a [28, 7, 12] 2 ; here 10; found a ....
D. M. Gordon. Minimal permutation sets for decoding the binary Golay codes. IEEE Trans. Inform. Theory, 28:541--543, 1982.
Permutation Decoding: An Update - Key (2003) (Correct)
....Now decode y as cg 1 i . Note that this is valid since permutations of the coordinate positions correspond to linear transformations of F , so that if y = x e, where x C, then yg = xg eg for any g S n , and if g Aut(C) then xg C. The next result is also in [9] and due to Gordon [7] using a formula of Schonheim [14] Result 2 If is a PD set for a t error correcting [n, k, d] q code C, and r = n k, then S # . ### . In Gordon [7] and Wolfman [16] small PD sets for the binary Golay codes were found. In Chabanne [6] abelian codes, i.e. ....
....= xg eg for any g S n , and if g Aut(C) then xg C. The next result is also in [9] and due to Gordon [7] using a formula of Schonheim [14] Result 2 If is a PD set for a t error correcting [n, k, d] q code C, and r = n k, then S # . ### . In Gordon [7] and Wolfman [16] small PD sets for the binary Golay codes were found. In Chabanne [6] abelian codes, i.e. ideals in the group algebra of an abelian group, are looked at using Groebner bases, and the ideas of permutation decoding are generalized. In general it is rather hard to find these PD sets, ....
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D. M. Gordon. Minimal permutation sets for decoding the binary Golay codes. IEEE Trans. Inform. Theory, 28:541--543, 1982.
On the Complexity of Minimum Distance Decoding of Long.. - Barg, Krouk, van Tilborg (1999) (Correct)
....the transmitted word from the received word Therefore, information set decoding can be accomplished by successively inspecting information sets of and encoding the corresponding parts of the received vector However, actually finding the set is very difficult. A few nontrivial examples are found in [21], 30] and [25] see also [4] Therefore, to implement the general information set decoding algorithm, we have to specify a way of choosing information sets. One obvious suggestion is to take random uniformly distributed subsets of We call the following algorithm covering set decoding because it, ....
D. M. Gordon, "Minimal permutation sets for decoding the binary Golay code," IEEE Trans. Inform. Theory, vol. IT-28, pp. 541--543, May 1982.
Soft Decoding Techniques for Codes and Lattices, Including.. - Conway, Sloane (1986) (5 citations) (Correct)
.... and vector quantizing 3 (see the references already mentioned, and [12] 13] 21] 27] 36] 37] 64] It is worth mentioning that there is already a considerable literature devoted to hard decision or conventional binary decoding of the Golay code ( 50, Chapter 16, 9] 5] 31] [39], 70] 71] Notation. Two codes or lattices and are geometrically similar if one can be obtained from the other by (possibly) a translation, rotation, reflection and change of scale. The direct sum [50, p. 76] of two codes or lattices and is written . The componentwise product of ....
D. M. Gordon, Minimal permutation sets for decoding the binary Golay code, IEEE Trans. Information Theory, IT-28 (1982), 541-543.
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D. M. Gordon. Minimal permutation sets for decoding the binary Golay codes. IEEE Trans. Inform. Theory, 28:541--543, 1982.
Affine Invariant Extended Cyclic Codes over Galois Rings - Dey, Rajan (2003) (Correct)
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D. M. Gordon, \Minimal permutation sets for decoding the binary golay codes," IEEE Trans. Inform. Theory, vol. 28, pp. 541-543, 1982.
Complexity Issues in Coding Theory - Barg (1997) (5 citations) (Correct)
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D. M. Gordon, "Minimal permutation sets for decoding the binary Golay code," IEEE Trans. Inform. Theory, IT-28 (3) (1982), 541--543.
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