75 citations · 282 across the 16 of their papers we have counts for
17 papers
The Covering Radius of the Reed-Muller Code in
Randall Dougherty, R. Daniel Mauldin, Mark Tiefenbruck
We present methods for computing the distance from a Boolean polynomial on variables of degree (i.e., a member of the Reed-Muller code ) to the space of lower-…
Network routing on regular directed graphs from spanning factorizations
Randall Dougherty, Vance Faber
Networks with a high degree of symmetry are useful models for parallel processor networks. In earlier papers, we defined several global communication tasks (universal exchange, uni…
Characteristic-Dependent Linear Rank Inequalities with Applications to Network Coding
Randall Dougherty, Eric Freiling, Kenneth Zeger
Two characteristic-dependent linear rank inequalities are given for eight variables. Specifically, the first inequality holds for all finite fields whose characteristic is not thre…
Achievable Rate Regions for Network Coding
Randall Dougherty, Chris Freiling, Kenneth Zeger
Determining the achievable rate region for networks using routing, linear coding, or non-linear coding is thought to be a difficult task in general, and few are known. We describe…
Translating the Cantor set by a random
Randall Dougherty, Jack Lutz, R. Daniel Mauldin +1
We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set "cancels randomness" in the sense that some of its members, when added to M…
Non-Shannon Information Inequalities in Four Random Variables
Randall Dougherty, Chris Freiling, Kenneth Zeger
Any unconstrained information inequality in three or fewer random variables can be written as a linear combination of instances of Shannon's inequality I(A;B|C) >= 0 . Such inequal…