Information on Result #684694
Linear OA(775, 117658, F7, 15) (dual of [117658, 117583, 16]-code), using construction XX applied to Ce(14) ⊂ Ce(12) ⊂ Ce(11) 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(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(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(71, 8, F7, 1) (dual of [8, 7, 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, 61060, F7, 2, 15) (dual of [(61060, 2), 122045, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(775, 61060, F7, 3, 15) (dual of [(61060, 3), 183105, 16]-NRT-code) | [i] | ||
| 3 | Digital (60, 75, 61060)-net over F7 | [i] | ||
| 4 | Linear OOA(775, 58829, F7, 2, 15) (dual of [(58829, 2), 117583, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(775, 39219, F7, 3, 15) (dual of [(39219, 3), 117582, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(775, 16808, F7, 15, 15) (dual of [(16808, 15), 252045, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |