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A geometric construction of an optimal [67,9,30] binary code

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2 Author(s)
Cossidente, A. ; Dipt. di Matematica, Univ. della Basilicata, Potenza, Italy ; Siciliano, A.

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)

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 3 )