A close relationship between the coding theory and the design theory has been studied by many researchers. The principal concern is directed to the designs formed by minimal weight codewords or very small weight codew...
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A close relationship between the coding theory and the design theory has been studied by many researchers. The principal concern is directed to the designs formed by minimal weight codewords or very small weight codewords. In the present article we study more designs. We extend the concept of the incidence relation, one of which is a classical one and the other is a dual one to the classical one in a certain sense. In the present article we focus on the binary golay code of length 24. But the idea will be applied to a wide class of self-dual codes such as self-dual extremal binarycodes or self-dual extremal ternary codes.
In this letter, two weak general error locator polynomials are proposed to improve the one-step decoding of the (23, 12, 7) binary golay code. Experimental results show that the presented decoders significantly reduce...
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In this letter, two weak general error locator polynomials are proposed to improve the one-step decoding of the (23, 12, 7) binary golay code. Experimental results show that the presented decoders significantly reduce the area compared to the existing one-step decoders.
Tail-biting-trellis representations of codes allow for iterative decoding algorithms, which are limited in effectiveness by the presence of pseudocodewords. We introduce a multivariate weight enumerator that keeps tra...
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Tail-biting-trellis representations of codes allow for iterative decoding algorithms, which are limited in effectiveness by the presence of pseudocodewords. We introduce a multivariate weight enumerator that keeps track of these pseudocodewords. This enumerator is invariant under many linear transformations, often enabling us to compute it exactly. The extended binary golay code has a particularly nice tail-biting-trellis and a famous unsolved question is to determine its minimal AWGN pseudodistance. The new enumerator provides an inroad to this problem.
We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 2(36), 24) code as the image of a Z(8)-linear Hensel lift of the binary golay code. The union of this code with a relevant c...
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We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96, 2(36), 24) code as the image of a Z(8)-linear Hensel lift of the binary golay code. The union of this code with a relevant coset yields a (96, 2(37), 24) code. The tables in [2], and [12] show that this rode and some of its shortenings are better than the best (non)linear binarycodes known so far. For instance, the best earlier known code of length 96 and minimum distance 24 had 2(33) words.
A decoding algorithm based on revised syndromes to decode the binary (23,12,7) golaycode is presented. The algorithm strongly depends on the algebraic properties of the code. For the algorithm, the worst complexity i...
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A new algorithm for maximum likelihood decoding of the Leech lattice is presented. The algorithm involves projecting the points of the Leech lattice directly onto the codewords of the (6,3,4) quaternary code-the hexac...
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A new algorithm for maximum likelihood decoding of the Leech lattice is presented. The algorithm involves projecting the points of the Leech lattice directly onto the codewords of the (6,3,4) quaternary code-the hexacode. Projection on the hexacode induces a partition of the Leech lattice into four cosets of a certain sublattice Q24. Such a partition into cosets enables maximum likelihood decoding of the Leech lattice with 3595 real operations in the worst case and only 2955 operations on the average. This is about half the worst case and the average complexity of the best previously known algorithm [3]. Moreover the proposed decoder is far simpler, both conceptually and structurally, than the state of the art decoder of [3].
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