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Matrix characterization of MDS linear codes over modules

✍ Scribed by Xue-Dong Dong; Cheong Boon Son; Erry Gunawan

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
205 KB
Volume
277
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let R be a commutative ring with identity, N be an R-module, and M = (a,/),.Γ—~. be a matrix over R. A linear code C of length n over N is defined to be a submodule of N '~. It is shown that a linear code C(k, r) with parity check matrix (-MI/,.) is maximum distance separable (MDS) iff the determinant of every h Γ— h submatrix, h = 1,2,..., rain{k, r}, of M is not an annihilator of any nonzero element of N. This characterization is used to derive some results for group codes over abelian groups.

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