2021/10/19 by Stanislav S. Malakhov, Malakhov, Stanislav S.
Computer Science · Engineering · #15B33 #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Mathematics #Formal Methods in Verification #Numerical Analysis (math.NA) #VLSI and Analog Circuit Testing #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2110.13325
openalex publication_date 2021/10/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The present paper focuses on the construction of a set of submatrices of a\ncirculant matrix such that it is a smaller set to verify that the circulant\nmatrix is an MDS (maximum distance separable) one, comparing to the complete\nset of square submatrices needed in general case. The general MDS verification\nmethod requires to test for singular submatrices: if at least one square\nsubmatrix is singular the matrix is not MDS. However, the complexity of the\ngeneral method dramatically increases for matrices of a greater dimension. We\ndevelop an algorithm that constructs a smaller subset of submatrices thanks to\na simple structure of circulant matrices. The algorithm proposed in the paper\nreduces the size of the testing set by approximately two matrix orders.\n