It has been known since [Zyablov and Pinsker 1982] that a random q-ary code of rate 1 − Hq(ρ) − ε (where 0 < ρ < 1 − 1/q, ε > 0 and Hq(·) is the q-ary entropy ...
We prove that binary linear concatenated codes with an outer algebraic code (specifically, a folded Reed-Solomon code) and independently and randomly chosen linear inner codes ach...
We study the local testability of linear codes. We first reformulate this question in the language of tolerant linearity testing under a non-uniform distribution. We then study th...