Information on Result #840803
Linear OOA(7107, 2882406, F7, 2, 16) (dual of [(2882406, 2), 5764705, 17]-NRT-code), using OOA 2-folding based on linear OA(7107, 5764812, F7, 16) (dual of [5764812, 5764705, 17]-code), using
- construction XX applied to Ce(15) ⊂ Ce(14) ⊂ Ce(12) [i] based on
- linear OA(7105, 5764801, F7, 16) (dual of [5764801, 5764696, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(797, 5764801, F7, 15) (dual of [5764801, 5764704, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(789, 5764801, F7, 13) (dual of [5764801, 5764712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(70, 9, F7, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(7107, 2882406, F7, 3, 16) (dual of [(2882406, 3), 8647111, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (91, 107, 2882406)-net over F7 | [i] | ||