Information on Result #684634
Linear OA(725, 117655, F7, 5) (dual of [117655, 117630, 6]-code), using construction X applied to Ce(4) ⊂ Ce(3) based on
- linear OA(725, 117649, F7, 5) (dual of [117649, 117624, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(719, 117649, F7, 4) (dual of [117649, 117630, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(70, 6, F7, 0) (dual of [6, 6, 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
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(725, 117655, F7, 2, 5) (dual of [(117655, 2), 235285, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(725, 117655, F7, 3, 5) (dual of [(117655, 3), 352940, 6]-NRT-code) | [i] | ||
| 3 | Digital (20, 25, 117655)-net over F7 | [i] | ||
| 4 | Linear OOA(725, 58827, F7, 2, 5) (dual of [(58827, 2), 117629, 6]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(725, 58827, F7, 3, 5) (dual of [(58827, 3), 176456, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 6 | Linear OOA(725, 58827, F7, 5, 5) (dual of [(58827, 5), 294110, 6]-NRT-code) | [i] | ||