Information on Result #1551736
Linear OOA(757, 117665, F7, 3, 11) (dual of [(117665, 3), 352938, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(757, 117665, F7, 11) (dual of [117665, 117608, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(756, 117663, F7, 11) (dual of [117663, 117607, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(755, 117649, F7, 11) (dual of [117649, 117594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(743, 117649, F7, 9) (dual of [117649, 117606, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(713, 14, F7, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,7)), using
- dual of repetition code with length 14 [i]
- linear OA(71, 14, F7, 1) (dual of [14, 13, 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(756, 117664, F7, 10) (dual of [117664, 117608, 11]-code), using Gilbert–Varšamov bound and bm = 756 > Vbs−1(k−1) = 120013 508722 005208 927485 790349 088061 237100 632759 [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(756, 117663, F7, 11) (dual of [117663, 117607, 12]-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(757, 58832, F7, 15, 11) (dual of [(58832, 15), 882423, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |