A q-ary error-correcting code C ⊆ {1, 2, . . . , q}n is said to be list decodable to radius ρ with list size L if every Hamming ball of radius ρ contains at most L codewords o...
Abstract. Given an algebraic geometry code CL(D, P), the GuruswamiSudan algorithm produces a list of all codewords in CL(D, P) within a specified distance of a received word. The i...
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 study the complexity of locally list-decoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that co...
: We study the weight distribution and list-decoding size of Reed-Muller codes. Given a weight parameter, we are interested in bounding the number of Reed-Muller codewords with a w...