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.
Visually evoked responses (VERs), CSF IgG/albumin ratio and CSF oligoclonal IgG were examined in 136 patients with multiple sclerosis (MS) admitted to hospital for investigation, and compared to the CSF findings in 87 patients with other neurological diseases (OND). 33% of patients with OND had abnormal CSF IgG/albumin ratios but only 9% had CSF oligoclonal… (More)
The Cambridge Low Contrast Gratings (CLCG) were used to assess contrast sensitivity (CS) in 39 patients with clinically definite multiple sclerosis and 60 control subjects. CS was determined in both horizontal and vertical orientations and compared with visual evoked responses (VERs) in the same populations. Only 33% of patients had abnormal CS whereas 82%… (More)
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)