Serdica Mathematical Journal

Volume 46, Number 3, 2020

C O N T E N T S

A B S T R A C T S

THE NON-EXISTENCE OF [383,5,286] AND [447,5,334] QUATERNARY LINEAR CODES
Hitoshi Kanda jinza80kirisame@gmail.com

2020 Mathematics Subject Classification: 94B27, 94B65, 94B05, 51E21.
Key words: optimal linear code, Griesmer bound, geometric method, quaternary linear code.

It is known that n₄(5, 286) = 383 or 384 and n₄(5, 334) = 447 or 448, where n_q(k,d) is the minimum length n for which an [n,k,d]_q code exists. We prove the non-existence of [383,5,286]₄ and [447,5,334]₄ codes, which determine the exact value of n₄(5,d) for d = 286, 334.

ON THE CHOW GROUPS OF HYPERSURFACES IN SYMPLECTIC GRASSMANNIANS
Robert Laterveer robert.laterveer@math.unistra.fr

2020 Mathematics Subject Classification: Primary 14C15, 14C25, 14C30.
Key words: Algebraic cycles, Chow groups, motive, Bloch-Beilinson conjectures.

Let Y be a Plücker hypersurface in a symplectic Grassmannian I₁ Gr(3, n) or a bisymplectic Grassmannian I₂ Gr(3, n). We show that many Chow groups of Y inject into cohomology.

2020 Mathematics Subject Classification: 05C50.
Key words: Strongly regular graph, magic square, conference graph.

We say that a regular graph G of order n and degree r ≥ 1 (which is not the complete graph) is strongly regular if there exist non-negative integers τ and θ such that |S_i ∩ S_j| = τ for any two adjacent vertices i and j and |S_i ∩ S_j| = θ for any two distinct non-adjacent vertices i and j, where S_k denotes the neighborhood of the vertex k. Using a method for constructing the magic and semi-magic squares of order 2k + 1, we have created two infinite classes of strongly regular graphs (i) strongly regular graph of order n = (2k + 1)² and degree r = 8k with τ = 2k + 5 and θ = 12 and (ii) strongly regular graph of order n = (2k + 1)² and degree r = 6k with τ = 2k + 1 and θ = 6 for k ≥ 2.

WHEN THE WEDDERBURN DECOMPOSITION OF THE SEMISIMPLE GROUP ALGEBRA F_qG IMPLIES THAT OF F_q(G× C₂)?
Gaurav Mittal gmittal@ma.iitr.ac.in,
R. K. Sharma rksharmaiitd@gmail.com

2020 Mathematics Subject Classification: 20C05.
Key words: Wedderburn decomposition, group algebra.

In this short note we give a condition under which the Wedderburn decomposition (WD) of the semisimple group algebra F_q(G× C₂) can be directly deduced from the WD of the semisimple group algebra F_qG, where F_q is a finite field with char(F_q) >2 , G is an arbitrary finite group and C₂ is a group of order 2. To complement the abstract theory with an example, we determine the WD of the semisimple group algebra F_q(A₅× C₂), where A₅ is the alternating group from that of F_qA₅.

STRONG CONVERSE INEQUALITIES FOR THE WEIGHTED SIMULTANEOUS APPROXIMATION BY THE SZÁSZ-MIRAKJAN OPERATOR
Borislav R. Draganov bdraganov@fmi.uni-sofia.bg

2020 Mathematics Subject Classification: 41A17, 41A25, 41A27, 41A28, 41A35, 41A40, 41A81.
Key words: Szász-Mirakjan operator, strong converse inequality, converse estimate, simultaneous approximation, modulus of smoothness, K-functional.

We establish two-term strong converse estimates of the rate of weighted simultaneous approximation by the Szász-Mirakjan operator for smooth functions in the supremum norm on the non-negative semi-axis. We consider Jacobi-type weights. The estimates are stated in terms of appropriate moduli of smoothness or K-functionals.

GENERALIZED HELICOIDAL SURFACES IN MINKOWSKI 5-SPACE
Ali Uçum aliucum05@gmail.com,
Makoto Sakaki sakaki@hirosaki-u.ac.jp

2020 Mathematics Subject Classification: 53C42, 53C50.
Key words: Minkowski 5-space, helicoidal surface, minimal surface, flat surface, normal curvature tensor.

In this paper, we study generalized helicoidal surfaces in Minkowski 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Minkowski 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the behavior of solutions.