Information on Result #1302361
Linear OA(7108, 5764854, F7, 15) (dual of [5764854, 5764746, 16]-code), using construction X with Varšamov bound based on
- linear OA(7106, 5764850, F7, 15) (dual of [5764850, 5764744, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- linear OA(797, 5764801, F7, 15) (dual of [5764801, 5764704, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(757, 5764801, F7, 9) (dual of [5764801, 5764744, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(79, 49, F7, 5) (dual of [49, 40, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- linear OA(7106, 5764852, F7, 14) (dual of [5764852, 5764746, 15]-code), using Gilbert–Varšamov bound and bm = 7106 > Vbs−1(k−1) = 16290 160193 567063 579736 169665 995478 282667 000900 149177 082832 870450 371358 439389 617583 616727 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 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: 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(7108, 2882427, F7, 2, 15) (dual of [(2882427, 2), 5764746, 16]-NRT-code) | [i] | OOA Folding | |