Information on Result #684706
Linear OA(737, 117656, F7, 7) (dual of [117656, 117619, 8]-code), using construction X4 applied to C([1,7]) ⊂ C([1,5]) based on
- linear OA(736, 117648, F7, 7) (dual of [117648, 117612, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(730, 117648, F7, 5) (dual of [117648, 117618, 6]-code), using the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(77, 8, F7, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using
- dual of repetition code with length 8 [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
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(737, 117656, F7, 2, 7) (dual of [(117656, 2), 235275, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(737, 117656, F7, 3, 7) (dual of [(117656, 3), 352931, 8]-NRT-code) | [i] | ||
| 3 | Digital (30, 37, 117656)-net over F7 | [i] | ||
| 4 | Linear OOA(737, 58828, F7, 2, 7) (dual of [(58828, 2), 117619, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(737, 39218, F7, 3, 7) (dual of [(39218, 3), 117617, 8]-NRT-code) | [i] | ||
| 6 | Linear OOA(737, 39218, F7, 7, 7) (dual of [(39218, 7), 274489, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |