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On the ranks of Toeplitz matrices over finite fields

โœ Scribed by Geoffrey L. Price; Glenn H. Truitt

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
220 KB
Volume
294
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Let T be a skew-symmetric Toeplitz matrix with entries in a ยฎnite ยฎeld. For all positive integers n let n be the upper n ร‚ n corner of T, with nullity m n m n . The sequence fm n X n P Ng satisยฎes a unimodality property and is eventually periodic if the entries of T satisfy a periodicity condition. We compute the maximum value and the period of the nullity sequence for Toeplitz matrices of ยฎnite bandwidth. This sequence satisยฎes a certain symmetry condition about its maximal values. These results apply to give some information about the ranks of general skew-symmetric Toeplitz matrices with eventually periodic entries.

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