Information on Result #684635
Linear OA(719, 117655, F7, 4) (dual of [117655, 117636, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- 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(713, 117649, F7, 3) (dual of [117649, 117636, 4]-code or 117649-cap in PG(12,7)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(719, 117655, F7, 2, 4) (dual of [(117655, 2), 235291, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(719, 117655, F7, 3, 4) (dual of [(117655, 3), 352946, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(719, 58827, F7, 2, 4) (dual of [(58827, 2), 117635, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(719, 58827, F7, 3, 4) (dual of [(58827, 3), 176462, 5]-NRT-code) | [i] | OA Folding and Stacking | |