Information on Result #1442815
Linear OOA(7105, 117688, F7, 2, 19) (dual of [(117688, 2), 235271, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7105, 117688, F7, 19) (dual of [117688, 117583, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(7104, 117686, F7, 19) (dual of [117686, 117582, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(767, 117649, F7, 13) (dual of [117649, 117582, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(18) ⊂ Ce(12) [i] based on
- linear OA(7104, 117687, F7, 18) (dual of [117687, 117583, 19]-code), using Gilbert–Varšamov bound and bm = 7104 > Vbs−1(k−1) = 7 574133 061547 394473 440685 192163 884247 366266 476275 052210 838503 650260 291373 718069 231633 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 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(7104, 117686, F7, 19) (dual of [117686, 117582, 20]-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(7105, 58844, F7, 3, 19) (dual of [(58844, 3), 176427, 20]-NRT-code) | [i] | OOA Folding | |