In this paper, upper bounds on the minimum Euclidean weights of Type I codes over Z6 , and self-dual codes over Z8 and Z10 , are derived for modest lengths. The notion of extremality for Euclidean weights is also introduced. We construct new extremal self-dual codes over these rings. Most of these codes are obtained via the double circulant and quasitwisted constructions. New extremal odd unimo...

We studied the dynamic behavior of a single semiflexible ring in linear chain matrix based on coarse-grained model using molecular dynamics simulation approach. found that chains’ hollow centers are frequently filled with chains. However, as rigidity chains increases, arranged parallel to each other and temporary caged. As result, swing movement normal direction is significantly limited, relaxa...

Tumor cell invadopodia mediate degradation of matrix barriers. A new study now demonstrates that a ring of active RhoC focuses invadopodial protrusion and degradation by regulating cofilin activity.

We obtain an asymptotic upper bound for the minimal number of generators for a finite direct sum of matrix algebras with entries in a finite field. This produces an upper bound for a similar quantity for integer matrix rings. We obtain an exact formula for the minimal number of generators for a finite direct sum of 2-by-2 matrix algebras with entries in a finite field. As a consequence, we show...

Abstract—A systematic way of constructing Grassmannian codes endowed with the subspace distance as lifts of matrix codes over the prime field Fp is introduced. The matrix codes are Fp-subspaces of the ring M2(Fp) of 2 × 2 matrices over Fp on which the rank metric is applied, and are generated as onesided proper principal ideals by idempotent elements of M2(Fp). Furthermore a weight function on ...