100 research outputs found

    Optimal Binary Locally Repairable Codes via Anticodes

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    This paper presents a construction for several families of optimal binary locally repairable codes (LRCs) with small locality (2 and 3). This construction is based on various anticodes. It provides binary LRCs which attain the Cadambe-Mazumdar bound. Moreover, most of these codes are optimal with respect to the Griesmer bound

    Primal-dual distance bounds of linear codes with application to cryptography

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    Let N(d,d⊥)N(d,d^\perp) denote the minimum length nn of a linear code CC with dd and d⊥d^{\bot}, where dd is the minimum Hamming distance of CC and d⊥d^{\bot} is the minimum Hamming distance of C⊥C^{\bot}. In this paper, we show a lower bound and an upper bound on N(d,d⊥)N(d,d^\perp). Further, for small values of dd and d⊥d^\perp, we determine N(d,d⊥)N(d,d^\perp) and give a generator matrix of the optimum linear code. This problem is directly related to the design method of cryptographic Boolean functions suggested by Kurosawa et al.Comment: 6 pages, using IEEEtran.cls. To appear in IEEE Trans. Inform. Theory, Sept. 2006. Two authors were added in the revised versio
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