S. Blackburn

activity

20082023

most citedNon-overlapping codes

40 citations · 178 across the 25 of their papers we have counts for

collaborators

35 papers

math.GR2023

Subsets of free groups with distinct differences

Simon R. Blackburn, Emma Smith, Luke Stewart

Let $F_{n}$ be a free group of rank $n$ , with free generating set $X$ . A subset $D$ of $F_{n}$ is a \emph{Distinct Difference Configuration} if the differences $g^{- 1} h$ are distinct,…

math.CO2023

Permutations that separate close elements, and rectangle packings in the torus

Simon R. Blackburn, Tuvi Etzion

Let $n$ , $s$ and $k$ be positive integers. For distinct $i, j \in Z_{n}$ , define $∣∣ i, j ∣ ∣_{n}$ to be the distance between $i$ and $j$ when the elements of $Z_{n}$ are writ…

cs.IT2022

Constructions and bounds for codes with restricted overlaps

Simon R. Blackburn, Navid Nasr Esfahani, Donald L. Kreher +1

Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes…

cs.IT2022

The capacity of a finite field matrix channel

Simon R. Blackburn, Jessica Claridge

The Additive-Multiplicative Matrix Channel (AMMC) was introduced by Silva, Kschischang and Kötter in 2010 to model data transmission using random linear network coding. The input a…

math.CO2022

Permutations that separate close elements

Simon R. Blackburn

Let $n$ be a fixed integer with $n \geq 2$ . For $i, j \in Z_{n}$ , define $∣∣ i, j ∣ ∣_{n}$ to be the distance between $i$ and $j$ when the elements of $Z_{n}$ are written in a…

math.CO2021

The enumeration of finite rings

Simon R. Blackburn, K. Robin McLean

Let $p$ be a fixed prime. We show that the number of isomorphism classes of finite rings of order $p^{n}$ is $p^{α}$ , where $α = \frac{4}{27} n^{3} + O (n^{5/2})$ . This result was stated (with…