TU1.R7.3

An Explicit Construction of $q$-ary MDS Array Codes and Their Efficient Decoding

Jingjie Lv, Dongguan University of Technology, China; Weijun Fang, Shandong University, China; Shu-Tao Xia, Tsinghua University, China; Hanxu Hou, Dongguan University of Technology, China

Session:
Algebraic Decoding

Track:
1: Algebraic Aspects of Coding Theory

Location:
VIP

Presentation Time:
Tue, 9 Jul, 10:25 - 10:45

Session Chair:
Julia Lieb, Technical university Ilmenau
Abstract
In this short work, a new explicit construction of $q$-ary MDS array codes with multiple parities will be provided, whose code lengths can be up to $q^{m-1}$, where $m-1$ is the size of subpackage. As far as we know, this may be the first explicit construction of practical MDS array codes with such long code lengths for general $q$. In addition, to demonstrate the applicability of our MDS array codes, by the LU factorization of Vandermonde matrices, we present an efficient decoding method aimed at the erased errors, whose computational complexity is $O(m^2)$ in total. Furthermore, if one stores a small number of polynomials in advance or computes the syndrome in a scheduled algorithm, the decoding efficiency of these MDS array codes can be further improved.
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