Every finite projective plane of odd order has an associated self-dual binary code with parameters (2(q2 + q + q2 + q + 1, We also construct other related self-orthogonal and doubly-even codes, and the vectors of minimum weight. The weight enumerator polynomials for the planes of orders 3 and 5 are found. The boundary and coboundary maps are introduced.
This paper studies families of self-orthogonal codes over Z 4. We show that the simplex codes (Type α and Type β) are self-orthogonal. We partially answer the question of Z 4-linearity for the codes from projective planes of even order. A new family of self-orthogonal codes over Z 4 is constructed via projective planes of odd order. Properties such as… (More)
A formula for Glynn's hyperdeterminant detp (p prime) of a square matrix shows that the number of ways to decompose any integral doubly stochastic matrix with row and column sums p − 1 into p − 1 permutation matrices with even product, minus the number of ways with odd product, is 1 (mod p). It follows that the number of even Latin squares of order p − 1 is… (More)
There is polynomial function Xq in the entries of an m × m(q − 1) matrix over a field of prime characteristic p, where q = p h is a power of p, that has very similar properties to the determinant of a square matrix. It is invariant under multiplication on the left by a non-singular matrix, and under permutations of the columns. This gives a way to extend… (More)