Information on Result #1553182
Linear OOA(7102, 117680, F7, 3, 19) (dual of [(117680, 3), 352938, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7102, 117680, F7, 19) (dual of [117680, 117578, 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, 117679, F7, 18) (dual of [117679, 117578, 19]-code), using Gilbert–Varšamov bound and bm = 7101 > Vbs−1(k−1) = 7 565384 437219 426067 480276 568730 446189 335893 697625 338825 703901 140302 017593 890704 321873 [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(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(7102, 39226, F7, 21, 19) (dual of [(39226, 21), 823644, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |