Turbo codes, introduced by Berrou, Glavieux and Thitimajshima in 1993 [1], are widely used codes that exhibit excellent empirical results, i.e., the decoding algorithm produces a codeword very quickly. While turbo codes are very popular, theoretical analysis of their performance has been unsupportive. Codewords have extremely small minimum distance, and no one has been able to prove that the de...

For example, CH the family of Hamming code is a family of codes with ni = 2 − 1, ki = 2 − i − 1, di = 3 and R(CH) = 1, δ(CH) = 0. We will mostly work with family of codes from now on. This is necessary as we will study the asymptotic behavior of algorithms for codes, which does not make sense for a fixed code. For example, when we say we say that a decoding algorithm for a code C takes O(n) tim...

For example, CH the family of Hamming code is a family of codes with ni = 2 − 1, ki = 2 − i − 1, di = 3 and R(CH) = 1, δ(CH) = 0. We will mostly work with family of codes from now on. This is necessary as we will study the asymptotic behavior of algorithms for codes, which does not make sense for a fixed code. For example, when we say we say that a decoding algorithm for a code C takes O(n) tim...

An open question about Gabidulin codes is whether polynomial-time list decoding beyond half the minimum distance is possible or not. In this contribution, we give a lower and an upper bound on the list size, i.e., the number of codewords in a ball around the received word. The lower bound shows that if the radius of this ball is greater than the Johnson radius, this list size can be exponential...