Batch Codes from Affine Cartesian Codes and Quotient Spaces

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 up one more than dimension space.