Information on Result #1725446
Digital (72, 86, 274519)-net over F7, using net defined by OOA based on linear OOA(786, 274519, F7, 21, 14) (dual of [(274519, 21), 5764813, 15]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(786, 823558, F7, 3, 14) (dual of [(823558, 3), 2470588, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(786, 823559, F7, 3, 14) (dual of [(823559, 3), 2470591, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(786, 823559, F7, 14) (dual of [823559, 823473, 15]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(11) [i] based on
- linear OA(785, 823543, F7, 15) (dual of [823543, 823458, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(715, 16, F7, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,7)), using
- dual of repetition code with length 16 [i]
- linear OA(71, 16, F7, 1) (dual of [16, 15, 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(14) ⊂ Ce(11) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(786, 823559, F7, 14) (dual of [823559, 823473, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(786, 823559, F7, 3, 14) (dual of [(823559, 3), 2470591, 15]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.