Information on Result #684631
Linear OA(738, 117656, F7, 8) (dual of [117656, 117618, 9]-code), using construction X applied to Ce(7) ⊂ Ce(5) based on
- linear OA(737, 117649, F7, 8) (dual of [117649, 117612, 9]-code), using an extension Ce(7) of 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(731, 117649, F7, 6) (dual of [117649, 117618, 7]-code), using an extension Ce(5) of 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(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(738, 81188, F7, 2, 8) (dual of [(81188, 2), 162338, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(738, 81188, F7, 3, 8) (dual of [(81188, 3), 243526, 9]-NRT-code) | [i] | ||
| 3 | Digital (30, 38, 81188)-net over F7 | [i] | ||
| 4 | Linear OOA(738, 58828, F7, 2, 8) (dual of [(58828, 2), 117618, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(738, 39218, F7, 3, 8) (dual of [(39218, 3), 117616, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(738, 29414, F7, 8, 8) (dual of [(29414, 8), 235274, 9]-NRT-code) | [i] | OA Folding and Stacking | |