Information on Result #684985
Linear OA(731, 2409, F7, 9) (dual of [2409, 2378, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
- linear OA(729, 2401, F7, 9) (dual of [2401, 2372, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(721, 2401, F7, 6) (dual of [2401, 2380, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(731, 2355, F7, 2, 9) (dual of [(2355, 2), 4679, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(731, 2355, F7, 3, 9) (dual of [(2355, 3), 7034, 10]-NRT-code) | [i] | ||
| 3 | Digital (22, 31, 2355)-net over F7 | [i] | ||
| 4 | Linear OOA(731, 1204, F7, 2, 9) (dual of [(1204, 2), 2377, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(731, 803, F7, 3, 9) (dual of [(803, 3), 2378, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(731, 602, F7, 9, 9) (dual of [(602, 9), 5387, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |