Information on Result #1731410
Digital (53, 68, 19550)-net over F9, using net defined by OOA based on linear OOA(968, 19550, F9, 21, 15) (dual of [(19550, 21), 410482, 16]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(968, 58651, F9, 3, 15) (dual of [(58651, 3), 175885, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(968, 58652, F9, 3, 15) (dual of [(58652, 3), 175888, 16]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(968, 58652, F9, 15) (dual of [58652, 58584, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(968, 59062, F9, 15) (dual of [59062, 58994, 16]-code), using
- construction XX applied to Ce(14) ⊂ Ce(12) ⊂ Ce(11) [i] based on
- linear OA(966, 59049, F9, 15) (dual of [59049, 58983, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(951, 59049, F9, 12) (dual of [59049, 58998, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(91, 12, F9, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(14) ⊂ Ce(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(968, 59062, F9, 15) (dual of [59062, 58994, 16]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(968, 58652, F9, 15) (dual of [58652, 58584, 16]-code), using
- discarding factors / shortening the dual code based on linear OOA(968, 58652, F9, 3, 15) (dual of [(58652, 3), 175888, 16]-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.