Information on Result #684692
Linear OA(781, 117658, F7, 16) (dual of [117658, 117577, 17]-code), using construction XX applied to Ce(15) ⊂ Ce(14) ⊂ Ce(12) based on
- linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(767, 117649, F7, 13) (dual of [117649, 117582, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(70, 7, F7, 0) (dual of [7, 7, 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(781, 67981, F7, 2, 16) (dual of [(67981, 2), 135881, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(781, 67981, F7, 3, 16) (dual of [(67981, 3), 203862, 17]-NRT-code) | [i] | ||
| 3 | Digital (65, 81, 67981)-net over F7 | [i] | ||
| 4 | Linear OOA(781, 58829, F7, 2, 16) (dual of [(58829, 2), 117577, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(781, 39219, F7, 3, 16) (dual of [(39219, 3), 117576, 17]-NRT-code) | [i] | ||