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.
Balanced Sparsest Generator Matrices for MDS Codes
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that given $n$ and $k$, for $q$ sufficiently large, there always exists an $[n, k]_q$ MDS code that has a generator matrix $G$ satisfying the following two conditions: (C1) Sparsest: each row of $G$ has Hamming weight $n - k + 1$; (C2) Balanced: Hamming weights of the columns of $G$ differ from each other by at most one.
fields
cs.IT 1years
2026 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
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.