| 1. |
- Löfvenberg, Jacob, 1971-
(författare)
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Binary Fingerprinting Codes
- 2005
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Ingår i: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 36:1, s. 69-81
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Tidskriftsartikel (refereegranskat)abstract
- Three binary fingerprinting code classes with properties similar to codes with the identifiable parent property are proposed. In order to compare such codes a new combinatorial quality measure is introduced. In the case of two cooperating pirates the measure is derived for the proposed codes, upper and lower bounds are constructed and the results of computer searches for good codes in the sense of the quality measure are presented. Some properties of the quality measure are also derived.
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| 2. |
- Anashin, Vladimir, et al.
(författare)
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T-functions revisited : new criteria for bijectivity/transitivity
- 2014
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Ingår i: Designs, Codes and Cryptography. - : Springer Netherlands. - 0925-1022 .- 1573-7586. ; 71:3, s. 383-407
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Tidskriftsartikel (refereegranskat)abstract
- The paper presents new criteria for bijectivity/transitivity of T-functions and a fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz p-adic functions and to study measure-preservation/ergodicity of these.
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| 3. |
- Avgustinovich, S. V., et al.
(författare)
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On intersection problem for perfect binary codes
- 2006
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Ingår i: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 39:3, s. 317-322
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Tidskriftsartikel (refereegranskat)abstract
- The main result is that to any even integer q in the interval 0 <= q <= 2(n+1-2) (log(n+1)), there are two perfect codes C-1 and C-2 of length n = 2(m) -1, m >= 4, such that vertical bar C-1 boolean AND C-2 vertical bar = q.
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| 4. |
- Avgustinovich, S. V., et al.
(författare)
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The classification of some perfect codes
- 2004
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Ingår i: Designs, Codes and Cryptography. - 0925-1022 .- 1573-7586. ; 31:3, s. 313-318
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Tidskriftsartikel (refereegranskat)abstract
- Perfect 1-error correcting codes C in Z(2)(n), where n = 2(m) - 1, are considered. Let [C] denote the linear span of the words of C and let the rank of C be the dimension of the vector space [C]. It is shown that if the rank of C is n - m + 2 then C is equivalent to a code given by a construction of Phelps. These codes are, in case of rank n - m + 2, described by a Hamming code H and a set of MDS-codes D-h; h is an element of H, over an alphabet with four symbols. The case of rank n - m + 1 is much simpler: Any such code is a Vasil'ev code.
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| 5. |
- Britz, Thomas, et al.
(författare)
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Demi-matroids from codes over finite Frobenius rings
- 2015
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Ingår i: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 75:1, s. 97-107
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Tidskriftsartikel (refereegranskat)abstract
- We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids. We also prove a MacWilliams-type identity for Hamming support enumerators of linear codes over finite Frobenius rings. As a special case, these results give a combinatorial proof of the MacWilliams identity for Hamming weight enumerators of linear codes over finite Frobenius rings.
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| 6. |
- Charpin, Pascale, et al.
(författare)
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Editorial : Special issue on coding and cryptography
- 2017
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Ingår i: Designs, Codes, and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 82:1, s. 1-2
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Tidskriftsartikel (refereegranskat)
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| 7. |
- Chen, Eric Zhi
(författare)
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A new iterative computer search algorithm for good quasi-twisted codes
- 2015
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Ingår i: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 76:2, s. 307-323
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Tidskriftsartikel (refereegranskat)abstract
- As a generalization to cyclic and consta-cyclic codes, quasi-twisted (QT) codes contain many good linear codes. During the last twenty years, a lot of record-breaking codes have been found by computer search for good QT codes. But due to the time complexity, very few QT codes have been reported recently. In this paper, a new iterative, heuristic computer search algorithm is presented, and a lot of new QT codes have been obtained. With these results, a total of 45 entries in the code tables for the best-known codes have been improved. Also, as an example to show the effectiveness of the algorithm, 8 better binary quasi-cyclic codes with dimension 12 and m = 13 than previously best-known results are constructed.
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| 8. |
- Chen, Eric Zhi
(författare)
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New binary h-generator quasi-cyclic codes by augmentation and new minimum distance bounds
- 2016
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Ingår i: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 80:1, s. 1-10
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Tidskriftsartikel (refereegranskat)abstract
- An [n, k, d] code is a binary linear code of block length n, dimension k and minimum Hamming distance d. Since the minimum distance determines the error detection or correction capability, it is desired that d is as large as possible for the given block length n and dimension k. One of the most fundamental problems in coding theory is to construct codes with best possible minimum distances. This problem is very difficult in both theory and practice. During the last decades, it has proved that the class of quasi-cyclic (QC) codes contain many such codes. In this paper, augmentation of binary QC codes is studied. A new augmentation algorithm is presented, and 10 new h-generator QC codes that are better than previously known code have been constructed. Furthermore, Construction X has been applied to obtain another 18 new improved binary linear codes.With the standard construction techniques, a total of 124 new binary linear codes that improve the lower bound on the minimum distance have been obtained.
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| 9. |
- Danev, Danyo, et al.
(författare)
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A family of constacyclic ternary quasi-perfect codes with covering radius 3
- 2011
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Ingår i: DESIGNS CODES AND CRYPTOGRAPHY. - : Springer Science Business Media. - 0925-1022 .- 1573-7586. ; 59:1-3, s. 111-118
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Tidskriftsartikel (refereegranskat)abstract
- In this paper a family of constacyclic ternary quasi-perfect linear block codes is presented. This family extends the result presented in a previous work by the first two authors, where the existence of codes with the presented parameters was stated as an open question. The codes have a minimum distance 5 and covering radius 3.
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| 10. |
- Danev, Danyo, 1973-, et al.
(författare)
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A Family of Ternary Quasi-Perfect BCH Codes
- 2008
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Ingår i: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 49, s. 265-271
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a family of ternary quasi-perfect BCH codes. These codes are of minimum distance 5 and covering radius 3. The first member of this family is the ternary quadratic-residue code of length 13.
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