A letter matrix is an n-by-n matrix whose entries are n symbols, each appearing n times. The row (column) distribution of a letter matrix is an n-by-n nonnegative integer matrix that tells how many of each letter are in each row (column). A row distribution R and a column distribution C are compatible if there exits a letter matrix A whose row distribution is R and whose column distribution is ...

Article history: Received 29 September 2008 Accepted 6 January 2009 Available online 14 February 2009 Submitted by R.A. Brualdi Dedicated to the memory of a great scholar and a valued friend, Professor David Gale. AMS classification: 90C20 90C33 15A39 15A63

Nous étudions le nombre de cöıncidences des chiffres uns dans chaque paire de lignes différentes d’une matrice binaire et inversible dont toutes les lignes contiennent la même quantité d’unités. Nous présentons des bornes pour ce nombre, et nous démontrons que ces bornes peuvent être atteintes. Que la borne inférieure peut être réalisée est démontré par moyen des exemples. Quant à la borne supé...

As one can see, without several examples worked out with a pencil and paper, this formal definition is not very insightful. To understand where restricted patterns really originated from, we draw on visual imagery and replace “one-dimensional” permutations by “twodimensional” objects, matrices. In doing so, we shall violate the customary labeling of the top row as the “first” row of a matrix. I...

This paper is concerned with general analysis on the rank and row-redundancy of an array of circulants whose null space defines a QC-LDPC code. Based on the Fourier transform and the properties of conjugacy classes and Hadamard products of matrices, we derive tight upper bounds on rank and row-redundancy for general array of circulants, which make it possible to consider row-redundancy in const...