On a One-Parameter Family of Riordan Arrays and the Weight Distribution of MDS Codes
Paul Barry
School of Science
Waterford Institute of Technology
Ireland
Patrick Fitzpatrick
Department of Mathematics
University College Cork
Ireland
Abstract:
We use the formalism of the Riordan group to study a one-parameter
family of lower-triangular matrices related to
the weight distribution of maximum distance separable codes. We
obtain factorization results for these matrices. We then derive
alternative expressions for the weight distribution of MDS codes. We
define related weight ratios and show that they satisfy a certain
linear recurrence.
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(Concerned with sequences
A007318
A113310 and
A113311
.)
Received June 21 2007;
revised version received November 16 2007.
Published in Journal of Integer Sequences, November 20 2007.
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