Réunion d'été SMC 2026
Saint John, 5 - 8 juin 2026
Théorie des plans combinatoires
Org: Masoomeh Akbari (University of Ottawa), Kianoosh Shokri (University of Ottawa) et Brett Stevens (Carleton University)
[PDF]
Org: Masoomeh Akbari (University of Ottawa), Kianoosh Shokri (University of Ottawa) et Brett Stevens (Carleton University)
[PDF]
- MASOOMEH AKBARI, University of Ottawa
- TIM ALDERSON, University of New Brunswick, Saint John
Length-Maximal Nonlinear Codes with Given Singleton Defect--Structure and Bounds [PDF]
- TIM ALDERSON, University of New Brunswick, Saint John
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For a linear $[n,k,d]_q$ code, the columns of a generator matrix form a projective arc, and the maximum length is governed by the classical maximal-arc bound $n \le (s+1)(q+1)+k-2$, where $s$ is the Singleton defect. We show that this same bound holds for all $(n,q^k,d)_q$ codes, with no assumption of linearity. Codes attaining the bound, which we call length-maximal, are necessarily symbol-uniform and have a sharply constrained distance spectrum. They also satisfy a divisibility condition on $s$ that mirrors, but is weaker than, the condition forced on linear codes. An equivalent form of the bound yields an improved Singleton-type inequality that recovers and extends a result of Guerrini, Meneghetti, and Sala for binary systematic codes. When the defect is large, the bound tightens in discrete steps. We also identify several conditions under which nonlinear codes satisfy the Griesmer bound, and close with open problems, grounded by the central question: can genuinely nonlinear length-maximal codes exist for parameters where no linear codes do?
- SIMON BLACKBURN, Royal Holloway, University of London
- AMANDA CHAFEE, Carleton University
- JOY COOPER, University of Victoria
- PETER DANZIGER, Toronto Metropolitan University
- SHONDA DUECK, University of Winnipeg
- AARON DWYER, Carleton University
- MARIE ROSE JERADE, University of Ottawa
- SHUXING LI, University of Delaware
- WILLIAM MARTIN, Worcester Polytechnic Institute
- PRANGYA PARIDA, University of Ottawa
- DAVID PIKE, Memorial University of Newfoundland
Edge-connectivity of vertex-transitive hypergraphs [PDF]
- AMANDA CHAFEE, Carleton University
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A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices.
A classic theorem of Mader asserts that every connected vertex-transitive graph is maximally edge-connected.
We generalise this result to hypergraphs and show that every connected linear uniform vertex-transitive hypergraph is maximally edge-connected.
By using combinatorial designs,
we also show that if we relax either the linear or uniform conditions in this generalisation, then we can construct examples of vertex-transitive hypergraphs
which are not maximally edge-connected.
This is joint work with Andrea Burgess and Robert Luther.
- SAROBIDY RAZAFIMAHATRATRA, Carleton University
- SHAHRIYAR POURAKBAR SAFFAR, Memorial University
- KIANOOSH SKOKRI, University of Ottawa
- DOUG STINSON, University of Waterloo / Carleton University
- SOPHIE TOMLIN, University of Ottawa
- SHAHRIYAR POURAKBAR SAFFAR, Memorial University