Information on Result #684778
Linear OA(763, 16815, F7, 15) (dual of [16815, 16752, 16]-code), using construction X applied to Ce(14) ⊂ Ce(11) based on
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(751, 16807, F7, 12) (dual of [16807, 16756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(763, 10125, F7, 2, 15) (dual of [(10125, 2), 20187, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(763, 10125, F7, 3, 15) (dual of [(10125, 3), 30312, 16]-NRT-code) | [i] | ||
| 3 | Digital (48, 63, 10125)-net over F7 | [i] | ||
| 4 | Linear OOA(763, 8407, F7, 2, 15) (dual of [(8407, 2), 16751, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(763, 5605, F7, 3, 15) (dual of [(5605, 3), 16752, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(763, 2402, F7, 15, 15) (dual of [(2402, 15), 35967, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |