Affine Cartesian codes are defined by evaluating multivariate polynomials at a cartesian product of finite subsets field. In this work we examine properties these as batch codes. We consider the recovery sets to be points aligned on specific direction and buckets derived from cosets subspace ambient space evaluation points. able prove that under conditions, an affine code is satisfy query size ...

In this work, cyclic-skew-cyclic codes and sum-rank BCH are introduced. Cyclic-skew-cyclic characterized as left ideals of a suitable non-commutative finite ring, constructed using skew polynomials on top (or vice versa). Single generators such found, they used to construct generator matrices the corresponding codes. The notion defining set is introduced, pairs roots poynomials. A lower bound (...

Entanglement-assisted quantum error-correcting codes (EAQECCs) constructed from Reed–Solomon and BCH are considered in this work. It is provided a complete explicit formula for the parameters of EAQECCs coming any code, Hermitian metric, code with extension degree 2 consecutive cyclotomic cosets, both Euclidean metric. The main task work computation completely general c, minimum number required...

Distributed storage systems are mainly justified due to their ability to store data reliably over some unreliable nodes such that the system can have long term durability. Recently, regenerating codes are proposed to make a balance between the repair bandwidth and the storage capacity per node. This is achieved through using the notion of network coding approach. In this paper, a new variation ...