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.
On the rank of random matrices over finite fields
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
A novel lower bound is introduced for the full rank probability of random finite field matrices, where a number of elements with known location are identically zero, and remaining elements are chosen independently of each other, uniformly over the field. The main ingredient is a result showing that constraining additional elements to be zero cannot result in a higher probability of full rank. The bound then follows by "zeroing" elements to produce a block-diagonal matrix, whose full rank probability can be computed exactly. The bound is shown to be at least as tight and can be strictly tighter than existing bounds.
years
2026 2representative citing papers
For transitive matroids the probability that K independent samples from p are distinct and independent is quasi-concave and maximized at the uniform distribution on the ground set.
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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.
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Maximum Probability of Independence in Transitive Matroids
For transitive matroids the probability that K independent samples from p are distinct and independent is quasi-concave and maximized at the uniform distribution on the ground set.