On self-dual doubly-even extremal codes
Discrete Mathematics - Coding Theory
On error-correcting codes and invariant linear forms
SIAM Journal on Discrete Mathematics
Algorithms in invariant theory
Algorithms in invariant theory
A coding theoretic approach to extending designs
Discrete Mathematics
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
A Gleason formula for Ozeki polynomials
Journal of Combinatorial Theory Series A
On Harmonic Weight Enumerators of Binary Codes
Designs, Codes and Cryptography
Split Weight Enumerators for the Preparata Codes with Applicationsto Designs
Designs, Codes and Cryptography
| Hi-index | 0.00 |
Jacobi polynomials were introduced byOzeki in analogy with Jacobi forms of lattices. They are usefulto compute coset weight enumerators, and weight enumerators ofchildren. We determine them in most interesting cases in lengthat most 32, and in some cases in length 72.We use them to construct group divisible designs, packing designs,covering designs, and (t,r)-designs in the senseof Calderbank-Delsarte. A major tool is invariant theory of finitegroups, in particular simultaneous invariants in the sense ofSchur, polarization, and bivariate Molien series. A combinatorialinterpretation of the Aronhold polarization operator is given.New rank parameters for spaces of coset weight distributionsand Jacobi polynomials are introduced and studied here.