Random [n,k] linear codes over F_q are MDS with probability tending to 1 if binom(n,k)/q -> 0 and to 0 if it -> infinity, with matching thresholds for super-regular matrices and Poisson limits e^{-lambda} in intermediate regimes.
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Probability of super-regular matrices and MDS codes over finite fields
Random [n,k] linear codes over F_q are MDS with probability tending to 1 if binom(n,k)/q -> 0 and to 0 if it -> infinity, with matching thresholds for super-regular matrices and Poisson limits e^{-lambda} in intermediate regimes.