23 citations · 49 across the 5 of their papers we have counts for
5 papers
Probability of super-regular matrices and MDS codes over finite fields
Rathinakumar Appuswamy, Marco Bazzani, Spencer Congero +3
Let be an linear code chosen uniformly at random over a finite field of size . The following asymptotic probability of being maximum distance sepa…
Capacity and Achievable Rate Regions for Linear Network Coding over Ring Alphabets
Joseph Connelly, Kenneth Zeger
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of n…
Linear Network Coding over Rings, Part I: Scalar Codes and Commutative Alphabets
Joseph Connelly, Kenneth Zeger
Fixed-size commutative rings are quasi-ordered such that all scalar linearly solvable networks over any given ring are also scalar linearly solvable over any higher-ordered ring. A…
Linear Network Coding over Rings, Part II: Vector Codes and Non-Commutative Alphabets
Joseph Connelly, Kenneth Zeger
We prove the following results regarding the linear solvability of networks over various alphabets. For any network, the following are equivalent: (i) vector linear solvability ove…
A Class of Non-Linearly Solvable Networks
Joseph Connelly, Kenneth Zeger
For each integer , a network is constructed which is solvable over an alphabet of size but is not solvable over any smaller alphabets. If is composite, then the n…