Lower rate bounds for Hermitian-lifted codes in odd prime characteristic

We prove that (q2, 2)-arcs exist in the projective Hjelmslev plane PHG(2, R) over a chain ring R of length 2, order |R| = q2 and prime characteristic. For odd prime characteristic, our construction solves the maximal arc problem. For characteristic 2, an extension of the above construction yields the lower bound q2 + 2 on the maximum size of a 2-arc in PHG(2, R). Translating the arcs into codes, we get linear [q3, 6, q3 −q2 −q] codes over \({\mathbb {F}_q}\) for every prime power q > 1 and linear [q3 + q, 6,q3 −q2 −1] codes over \({\mathbb {F}_q}\) for the special case q = 2r. Furthermore, we construct 2-arcs of size (q + 1)2/4 in the planes PHG(2, R) over Galois rings R of length 2 and odd characteristic p2.

Differential spectrum of some power functions in odd prime characteristic

Comtrans algebras, as analogues of Lie algebras, provide tangent bundle structure corresponding to web geometry in a manifold. In this article, restricted comtrans algebras over rings of small odd prime characteristic are introduced, as analogues of restricted Lie algebras. It is shown that their representations are equivalent to modules over a restricted universal enveloping algebra.

First degree cohomology of Specht modules over fields of odd prime characteristic

The failure of the schizophrenia concept and the argument for its replacement by hebephrenia: applying the medical model for disease recognition