Information on Result #1442721
Linear OOA(7103, 117682, F7, 2, 19) (dual of [(117682, 2), 235261, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7103, 117682, F7, 19) (dual of [117682, 117579, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(7101, 117678, F7, 19) (dual of [117678, 117577, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(797, 117650, F7, 19) (dual of [117650, 117553, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(773, 117650, F7, 15) (dual of [117650, 117577, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(74, 28, F7, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,7)), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(7101, 117680, F7, 18) (dual of [117680, 117579, 19]-code), using Gilbert–Varšamov bound and bm = 7101 > Vbs−1(k−1) = 7 566477 494903 534340 314654 930375 305747 835375 897299 411454 002532 354326 885301 636888 100151 [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(7101, 117678, F7, 19) (dual of [117678, 117577, 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(7103, 58841, F7, 3, 19) (dual of [(58841, 3), 176420, 20]-NRT-code) | [i] | OOA Folding | |