Generalized ovals, 2.5-dimensional additive codes, and multispreads

Title data

Krotov, Denis ; Kurz, Sascha:
Generalized ovals, 2.5-dimensional additive codes, and multispreads.
Bayreuth , 2025 . - 68 p.
DOI: https://doi.org/10.15495/EPub_UBT_00008703

Official URL:

Abstract in another language

We present constructions and bounds for additive codes over a finite field in terms of their geometric counterpart, i.e. projective systems. It is known that the maximum number of (l-1)-spaces in PG(2,q), such that no hyperplane contains three, is given by q^l+1 if q is odd. Those geometric objects are called generalized ovals. We show that cardinality q^l+2 is possible if we decrease the dimension a bit. We completely determine the minimum possible lengths of additive codes over GF(9) of dimension 2.5 and give improved constructions for other small parameters. As an application, we consider multispreads in PG(4,q), in particular, completing the characterization of parameters of GF(4)-linear 64-ary one-weight codes.

Further data

Item Type:	Preprint, postprint
Keywords:	additive code; projective system; generalized oval; multispread; one-weight code; two-weight code
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science
Result of work at the UBT:	Yes
DDC Subjects:	000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics
Date Deposited:	22 Nov 2025 22:00
Last Modified:	25 Nov 2025 07:47
URI:	https://eref.uni-bayreuth.de/id/eprint/95307