We demonstrate that an MDS self-dual [16, 8, 9] code over Fp exists for an odd prime number p with 23 ≤ p ≤ 499 by constructing new MDS self-dual codes for the open cases. These codes are obtained using two construction methods based on negacirculant matrices. MDS self-dual [18, 9, 10] codes over Fp are also constructed for p = 53, 61, 73, 89, 97.

Minimum storage regenerating (MSR) codes form a special class of maximum distance separable (MDS) codes by providing mechanisms for exact regeneration of a single code block in their codewords by downloading the minimum amount of information from the remaining code blocks. As a result, the MSR codes find application to distributed storage systems to enable node repairs with the optimal repair b...

Two new families of good nonbinary quantum codes are constructed in this paper. The first one can be regarded as a generalization of [Theorem 3.2, X. Kai, S. Zhu and Y. Tang, Phys. Rev. A 88, 012326 (2013)], in the sense that we drop the constraint q ≡ 1 (mod 4). The later one is a quantum maximal-distance-separable (MDS) code. Compared the parameters of our quantum MDS codes with the parameter...

A q-ary maximum distance separable (MDS) code C with length n, dimension k over an alphabet A of size q is a set of qk codewords that are elements of An, such that the Hamming distance between two distinct codewords in C is at least n− k+1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to two-dimensional q-ary MDS codes, and q-ary one-error-correcting MDS codes for q ...

De nition. The reason for the title MDS is because of the tie with maximum distance separable codes. Indeed, a [n; k; d] linear code C is said to be maximum distance separable if it meets the Singleton Bound k n d + 1 at equality. This bound is simply proved by noting that in a code of distance d, any choice of n d+ 1 entries can determine at most one codeword of C, so in the case of equality, ...

The MacWilliams identity, which relates the weight distribution of a code to the weight distribution of its dual code, is useful in determining the weight distribution of codes. In this paper, we first provide an alternative proof to the MacWilliams identity for linear codes with the Hamming metric. An intermediate result of our approach is that the Hamming weight enumerator of the dual of any ...

For a positive integer $ b\ge2 $, the b $-symbol code is new coding framework proposed to combat $-errors in read channels. Especially, 2 called symbol-pair code. Remarkably, classical maximum distance separable (MDS) also an MDS Recently, for any \mathcal{C} Ma and Luo determined weight distribution of $. In this paper, by calculating number solutions some equations utilizing shortened codes w...

<p style='text-indent:20px;'>The intersection of a linear code and its dual is called the hull this code. The complementary (LCD) if dimension zero. In paper, we develop method to construct LCD codes with one-dimensional by association schemes. One constructions in paper generalizes that associated Gauss periods given [<xref ref-type="bibr" rid="b5">5</xref>]. addition, presen...

Upper bounds on Kq (n; R), the minimum number of codewords in a q-ary code of length n and covering radius R, are improved. Such bounds are obtained by constructing corresponding covering codes. In particular, codes of length q + 1 are discussed. Good such codes can be obtained from maximum distance separable (MDS) codes. Furthermore, they can often be combined eeectively with other covering co...

Low encoding/decoding complexity is essential for practical RAID-6 storage systems. In this paper, we describe a new coding scheme, which we call Rotary-code, for RAID-6 disk arrays. We construct Rotarycode based on a bit matrix-vector product similar to the Reed-Solomon coding, and provide the geometry encoding method and detailed non-recursive decoding algorithms. The capability of two-disk f...