We give further results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper [6], and suggests a version of a Singleton bound. We also present some families of codes meeting these new bounds.

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.

This study was carried out to examine aflatoxin B1 (AFB1) removal ability of four strains of lactic acidbacteria (LAB). Three indigenous (Lactobacillus rhamnosus TMU094, Lactobacillus fermentum TMU121and Pedioccus pentosaceus TMU457) and a non-indigenous (Labacillus rhamnosus PTCC1637) isolateswere studied. The strains were incubated with (AFB1) at different time. The toxin residual in the supe...

For self-dual codes with all weights divisible by an integer greater than one, the minimum distance is bounded by the Mallows-Sloane upper bounds and by their improvements due to Krasikov-Litsyn and Rains. We obtain the improved upper bounds from short relations with constant coefficients on suitable binomial moments of the codes. In this approach, the Mallows-Sloane bounds are analogues of the...

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

this study was carried out to examine aflatoxin b1 (afb1) removal ability of four strains of lactic acidbacteria (lab). three indigenous (lactobacillus rhamnosus tmu094, lactobacillus fermentum tmu121and pedioccus pentosaceus tmu457) and a non-indigenous (labacillus rhamnosus ptcc1637) isolateswere studied. the strains were incubated with (afb1) at different time. the toxin residual in the supe...

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...