Title :
A geometric construction of an optimal [67,9,30] binary code
Author :
Cossidente, Antonio ; Siciliano, Alessandro
Author_Institution :
Dipt. di Matematica, Univ. della Basilicata, Potenza, Italy
fDate :
3/1/2001 12:00:00 AM
Abstract :
We construct a new optimal binary [67,9,30]-code corresponding to a complete cap of PG(8,2). This cap is obtained by gluing together some Hermitian Veroneseans in a mixed partition of PG(8,2) and one hyperoval. We also construct a ternary [364,9,234]-code corresponding to a complete cap of PG(8,3). This cap turns out to be as large as the largest known cap in PG(8,3) (in an asymptotical sense)
Keywords :
binary codes; error correction codes; geometric codes; ternary codes; (364,9,234) ternary code; (67,9,30) binary code; Hermitian Veroneseans; complete cap; geometric construction; hyperoval; mixed partition; optimal binary code; projective geometry; Binary codes; Error correction codes; Galois fields; Hamming distance; Hamming weight; Linear code; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
