Information on Result #684695
Linear OA(775, 117664, F7, 14) (dual of [117664, 117589, 15]-code), using construction XX applied to Ce(14) ⊂ Ce(11) ⊂ Ce(10) based on
- 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(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(755, 117649, F7, 11) (dual of [117649, 117594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(71, 14, F7, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(775, 117664, F7, 2, 14) (dual of [(117664, 2), 235253, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(775, 117664, F7, 3, 14) (dual of [(117664, 3), 352917, 15]-NRT-code) | [i] | ||
| 3 | Digital (61, 75, 117664)-net over F7 | [i] | ||
| 4 | Linear OOA(775, 58832, F7, 2, 14) (dual of [(58832, 2), 117589, 15]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(775, 39221, F7, 3, 14) (dual of [(39221, 3), 117588, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(775, 16809, F7, 14, 14) (dual of [(16809, 14), 235251, 15]-NRT-code) | [i] | OA Folding and Stacking | |