IMath Webinar Series: Romar B. dela Cruz, Ph.D. and Homer Franz De Vera

You are all invited to attend the fifth webinar of the IMath Webinar Series on Monday, December 13, 2021, 2pm. Dr. Romar dela Cruz and Mr. Homer Franz De Vera will be our speakers.

Romar B. dela Cruz, Ph.D. (Coding and Number Theory Group)
Title: Minimal Codewords and Projective Geometry
Abstract: A nonzero codeword in a linear code is minimal if its support does not properly contain the support of another nonzero codeword. Minimal codewords have found applications in decoding and in cryptography. We present new results on the minimum number of minimal codewords in linear codes given the length and dimension.

Homer Franz C. De Vera (Discrete Geometry and Combinatorics Group)
Title: Quotient-complete arc-transitive latin square graphs associated with the general semilinear group of degree one
Abstract: A graph \(\Gamma\) with automorphism group \(G\leq\mbox{Aut}(\Gamma)\) is said to be \(G\)-arc-transitive if \(G\) acts transitively on ordered pairs of adjacent vertices of \(\Gamma\), and is said to be \(G\)-quotient-complete if every nontrivial quotient graph of \(\Gamma\) arising from orbits of some normal subgroup of \(G\) is a complete graph or an empty graph. We describe all pairs \((\Gamma, G)\) where \(\Gamma\) is a connected \(G\)-arc-transitive and \(G\)-quotient-complete graph arising from transitive subgroups of the one-dimensional general semilinear group \(\Gamma L_1(p^d)\), and \(\Gamma\) is a latin square graph of the Cayley table of an elementary abelian group \(C_p^d\). In the process, we also obtain an alternative description of the transitive subgroups of \(\Gamma L_1(p^d)\) that is equivalent to that given by D. Foulser in [2,3].
References:
[1] Amarra, C., Quotient-Complete Arc-Transitive Latin Square Graphs from Groups, Graphs and Combinatorics 34 (2018) pp. 1651-1669.
[2] D. A. Foulser, The flag-transitive collineation groups of the finite desarguesian affine planes, Canadian Journal of Mathematics, 16 (1964), pp. 443-472.
[3] D.A. Foulser and M.J. Kallaher, Solvable, flag-transitive, rank 3 collineation groups, Geometriae Dedicata, 7 (1978), pp. 111-130