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The Ethereal
The rank of random matrices over finite fields
October 17, 2018 · The Ethereal · 🏛 arXiv.org
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Authors
Amin Coja-Oghlan, Pu Gao
arXiv ID
1810.07390
Category
math.CO: Combinatorics
Cross-listed
cs.DM,
cs.IT
Citations
9
Venue
arXiv.org
Last Checked
2 months ago
Abstract
We determine the rank of a random matrix A over a finite field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula verifies a conjecture of Lelarge [Proc. IEEE Information Theory Workshop 2013]. The proofs are based on coupling arguments and the interpolation method from mathematical physics.
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