Information on Result #1731084
Digital (27, 39, 744)-net over F9, using net defined by OOA based on linear OOA(939, 744, F9, 15, 12) (dual of [(744, 15), 11121, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(939, 1489, F9, 3, 12) (dual of [(1489, 3), 4428, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(939, 1489, F9, 12) (dual of [1489, 1450, 13]-code), using
- 747 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0, 1, 32 times 0, 1, 79 times 0, 1, 144 times 0, 1, 207 times 0, 1, 264 times 0) [i] based on linear OA(931, 734, F9, 12) (dual of [734, 703, 13]-code), using
- construction XX applied to C1 = C([727,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([727,10]) [i] based on
- linear OA(928, 728, F9, 11) (dual of [728, 700, 12]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(928, 728, F9, 11) (dual of [728, 700, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(931, 728, F9, 12) (dual of [728, 697, 13]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(925, 728, F9, 10) (dual of [728, 703, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C([727,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([727,10]) [i] based on
- 747 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0, 1, 32 times 0, 1, 79 times 0, 1, 144 times 0, 1, 207 times 0, 1, 264 times 0) [i] based on linear OA(931, 734, F9, 12) (dual of [734, 703, 13]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(939, 1489, F9, 12) (dual of [1489, 1450, 13]-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.