Information on Result #684775
Linear OA(768, 16815, F7, 16) (dual of [16815, 16747, 17]-code), using construction X applied to Ce(15) ⊂ Ce(12) based on
- linear OA(766, 16807, F7, 16) (dual of [16807, 16741, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [i]
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(768, 11153, F7, 2, 16) (dual of [(11153, 2), 22238, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(768, 11153, F7, 3, 16) (dual of [(11153, 3), 33391, 17]-NRT-code) | [i] | ||
| 3 | Digital (52, 68, 11153)-net over F7 | [i] | ||
| 4 | Linear OOA(768, 5605, F7, 3, 16) (dual of [(5605, 3), 16747, 17]-NRT-code) | [i] | OOA Folding | |