Codes with the Same Weight Distributions as the Goethals Codes and the Delsarte-Goethals Codes
Designs, Codes and Cryptography
On t-designs from codes over Z4
Discrete Mathematics
Infinite Families of 3-Designs from Z4-Goethals Codes with Block Size 8
SIAM Journal on Discrete Mathematics
3-Designs from the Z4-Goethals Codes via a New Kloosterman Sum Identity
Designs, Codes and Cryptography
A simple proof to the minimum distance of Z4-linear Goethals-like codes
Journal of Complexity - Special issue on coding and cryptography
The algebraic decoding of the Z4-linear Goethals code
IEEE Transactions on Information Theory - Part 2
On algebraic decoding of the Z4-linear Goethals-like codes
IEEE Transactions on Information Theory
3-Designs from all Z4-Goethals-like codes with block size 7 and 8
Finite Fields and Their Applications
Exceptional Polynomials over Finite Fields
Finite Fields and Their Applications
3-Designs from all Z4-Goethals-like codes with block size 7 and 8
Finite Fields and Their Applications
| Hi-index | 0.00 |
We construct a family of simple 3-(2m,8,14(2m–8)/3) designs, with odd m≥5, from all Z4-Goethals-like codes ${\mathcal{G}}_k$ with k=2l and l≥1. In addition, these designs imply also the existence of the other design families constructed from the Z4-Goethals codes ${\mathcal{G}}_1$ by Ranto. In the existence proofs we count the number of solutions to certain systems of equations over finite fields and use Dickson polynomials and variants of cyclotomic polynomials and identities connecting them.