Information on Result #1442587
Linear OOA(7100, 117690, F7, 2, 18) (dual of [(117690, 2), 235280, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7100, 117690, F7, 18) (dual of [117690, 117590, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(798, 117686, F7, 18) (dual of [117686, 117588, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(77, 37, F7, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(798, 117688, F7, 17) (dual of [117688, 117590, 18]-code), using Gilbert–Varšamov bound and bm = 798 > Vbs−1(k−1) = 182 399347 647397 568005 117739 585778 309681 584529 696909 753113 273226 663512 594091 425911 [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
- linear OA(798, 117686, F7, 18) (dual of [117686, 117588, 19]-code), 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(7100, 58845, F7, 3, 18) (dual of [(58845, 3), 176435, 19]-NRT-code) | [i] | OOA Folding | |