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On a one-parameter family of Riordan arrays and the weight distribution of MDS codes. (English) Zbl 1145.11025

The authors consider a family of transformation matrices which can be related to the weight distribution of maximum distance separable (MDS) codes. They use the formalism of the Riordan group to study a one-parameter family of lower-triangular matrices related to the weight distribution of MDS codes. A factorization results for these matrices are obtained. Then, an alternative expressions for the weight distribution of MDS codes are derived. Also, the authors define related weight ratios and show that they satisfy a certain linear recurrence.

MSC:

11B83 Special sequences and polynomials
94B05 Linear codes (general theory)
11B65 Binomial coefficients; factorials; \(q\)-identities
11B37 Recurrences

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