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  • 1.
    Chen, Eric Zhi
    Kristianstad University, School of Health and Society, Avdelningen för Design och datavetenskap.
    A new iterative computer search algorithm for good quasi-twisted codes2015In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 76, no 2, p. 307-323Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Chen, Eric Zhi
    Kristianstad University, School of Health and Society, Avdelningen för Design och datavetenskap.
    New binary h-generator quasi-cyclic codes by augmentation and new minimum distance bounds2016In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 80, no 1, p. 1-10Article in journal (Refereed)
    Abstract [en]

    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.

  • 3.
    Chen, Wende
    et al.
    Academia Sinica and Key State Lab. of Information Security, Graduate School of Academia Sinica, Institute of Systems Science, Beijing.
    Chen, Eric Zhi
    Kristianstad University, School of Health and Society, Avdelningen för Design och datavetenskap.
    Klove, Torleiv
    Department of Informatics, University of Bergen.
    New constructions of disjoint distinct difference sets1998In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 15, no 2, p. 157-165Article in journal (Refereed)
    Abstract [en]

    New constructions of regular disjoint distinct difference sets (DDDS) are presented. In particular,multiplicative and additive DDDS are considered.

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