A new proof of the uniqueness and of the existence of the extended ternary golay code is presented. The proof connects the code to the projective plane of order 3 and is of an elementary nature. (C) 2002 Elsevier Scie...
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A new proof of the uniqueness and of the existence of the extended ternary golay code is presented. The proof connects the code to the projective plane of order 3 and is of an elementary nature. (C) 2002 Elsevier Science B.V. All rights reserved.
A new algebraic decoding algorithm for the ternary (11, 6, 5) golaycode is presented. The algorithm we present is based solely on the computation of the syndrome polynomials S(x) (without the evaluator and locator po...
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A new algebraic decoding algorithm for the ternary (11, 6, 5) golaycode is presented. The algorithm we present is based solely on the computation of the syndrome polynomials S(x) (without the evaluator and locator polynomial) and on the direct use of a Chien search directly over S(x). (C) 1998 Elsevier Science B.V. All rights reserved.
Goldberg constructed an MDS code over F-9 whose ternary image is the ternarygolay [12,6,6] code. Motivated by the work, in this paper, we found all such MDS codes over F-9 under some equivalence. (C) 2004 Elsevier B....
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Goldberg constructed an MDS code over F-9 whose ternary image is the ternarygolay [12,6,6] code. Motivated by the work, in this paper, we found all such MDS codes over F-9 under some equivalence. (C) 2004 Elsevier B.V. All rights reserved.
The depth distribution of a linear code was recently introduced by Etzion. In this correspondence, a number of basic and interesting properties for the depth of finite words and the depth distribution of linear codes ...
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The depth distribution of a linear code was recently introduced by Etzion. In this correspondence, a number of basic and interesting properties for the depth of finite words and the depth distribution of linear codes are obtained. In addition, we study the enumeration problem of counting the number of linear subcodes with the prescribed depth constraints, and derive some explicit and interesting enumeration formulas. Furthermore, we determine the depth distribution of Reed-Muller code RM (m, r). Finally, we show that there are exactly nine depth-equivalence classes for the ternary [11, 6, 5] golaycodes.
Using tensor product constructions for the first-order generalized Reed-culler codes, we extend the well-established concept of the Gray isometry between (Z(4), delta(L)) and (Z(2)(2), delta(H)) to the context of fini...
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Using tensor product constructions for the first-order generalized Reed-culler codes, we extend the well-established concept of the Gray isometry between (Z(4), delta(L)) and (Z(2)(2), delta(H)) to the context of finite chain rings. Our approach covers previous results by Carlet, Constantinescu, Nechaev et al, and overlaps with Heise et al. and Hanold ct ar. Applying the Gray isometry on Z(9) we Obtain a previously unknown nonlinear ternary (36, 3(12), 15) code.
A ternary [66, 10, 36](3)-code admitting the Mathieu group M-12 as a group of automorphisms has recently been constructed by N. Pace, see Pace (2014). We give a construction of the Pace code in terms of M-12 as well a...
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A ternary [66, 10, 36](3)-code admitting the Mathieu group M-12 as a group of automorphisms has recently been constructed by N. Pace, see Pace (2014). We give a construction of the Pace code in terms of M-12 as well as a combinatorial description in terms of the small Witt design, the Steiner system S(5, 6, 12). We also present a proof that the Pace code does indeed have minimum distance 36. (C) 2017 Elsevier B.V. All rights reserved.
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