Article history: Received 20 May 2010 Available online xxxx

This paper presents a new class of q-ary erasure-correcting codes based on Latin and Sudoku squares of order q, and an iterative decoding algorithm similar to the one used for the Low Density Parity Check code. The algorithm works by assigning binary variables to the q-ary values, and by generalizing the definition of parity check operation to represent the constraints that define the Latin and...

Applying results from partial difference sets, quadratic forms, and recent results of Brouwer and Van Dam, we construct the first known amorphic association scheme with negative Latin square type graphs and whose underlying set is a nonelementary abelian 2-group. We give a simple proof of a result of Hamilton that generalizes Brouwer’s result. We use multiple distinct quadratic forms to constru...

We answer a question posed by Dénes and Keedwell that is equivalent to the following. For each order n what is the smallest size of a partial latin square that cannot be embedded into the Cayley table of any group of order n? We also solve some variants of this question and in each case classify the smallest examples that cannot be embedded. We close with a question about embedding of diagonal ...

We study the behavior of heuristics based on the LP relaxation with respect to the underlying constraindness of the problem. Our study focuses on the Latin square (or quasigroup) completion problem [1]) as a prototype for highly combinatorial problems. We find that simple techniques based on the LP relaxation of the problem provide satisfactory guidance for underand over-constrained instances. ...