Information on Result #1740900
Digital (20, 34, 399)-net over F32, using net defined by OOA based on linear OOA(3234, 399, F32, 18, 14) (dual of [(399, 18), 7148, 15]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(3234, 1597, F32, 2, 14) (dual of [(1597, 2), 3160, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3234, 1599, F32, 2, 14) (dual of [(1599, 2), 3164, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3234, 1599, F32, 14) (dual of [1599, 1565, 15]-code), using
- 565 step Varšamov–Edel lengthening with (ri) = (3, 4 times 0, 1, 19 times 0, 1, 61 times 0, 1, 161 times 0, 1, 315 times 0) [i] based on linear OA(3227, 1027, F32, 14) (dual of [1027, 1000, 15]-code), using
- construction XX applied to C1 = C([1022,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([1022,12]) [i] based on
- linear OA(3225, 1023, F32, 13) (dual of [1023, 998, 14]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3225, 1023, F32, 13) (dual of [1023, 998, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3227, 1023, F32, 14) (dual of [1023, 996, 15]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([1022,12]) [i] based on
- 565 step Varšamov–Edel lengthening with (ri) = (3, 4 times 0, 1, 19 times 0, 1, 61 times 0, 1, 161 times 0, 1, 315 times 0) [i] based on linear OA(3227, 1027, F32, 14) (dual of [1027, 1000, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3234, 1599, F32, 14) (dual of [1599, 1565, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(3234, 1599, F32, 2, 14) (dual of [(1599, 2), 3164, 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.