Information on Result #1441673
Linear OOA(775, 5764821, F7, 2, 11) (dual of [(5764821, 2), 11529567, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(775, 5764821, F7, 11) (dual of [5764821, 5764746, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(774, 5764819, F7, 11) (dual of [5764819, 5764745, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(773, 5764801, F7, 11) (dual of [5764801, 5764728, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(717, 18, F7, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,7)), using
- dual of repetition code with length 18 [i]
- linear OA(71, 18, F7, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(774, 5764820, F7, 10) (dual of [5764820, 5764746, 11]-code), using Gilbert–Varšamov bound and bm = 774 > Vbs−1(k−1) = 195 284020 110664 029135 971672 884046 346856 765541 389552 560432 975319 [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(774, 5764819, F7, 11) (dual of [5764819, 5764745, 12]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(775, 2882410, F7, 3, 11) (dual of [(2882410, 3), 8647155, 12]-NRT-code) | [i] | OOA Folding | |