Information on Result #1734582
Digital (41, 60, 1052)-net over F16, using net defined by OOA based on linear OOA(1660, 1052, F16, 22, 19) (dual of [(1052, 22), 23084, 20]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(1660, 5261, F16, 2, 19) (dual of [(5261, 2), 10462, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1660, 5262, F16, 2, 19) (dual of [(5262, 2), 10464, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1660, 5262, F16, 19) (dual of [5262, 5202, 20]-code), using
- 1155 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 15 times 0, 1, 54 times 0, 1, 151 times 0, 1, 337 times 0, 1, 589 times 0) [i] based on linear OA(1652, 4099, F16, 19) (dual of [4099, 4047, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(1652, 4096, F16, 19) (dual of [4096, 4044, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1649, 4096, F16, 18) (dual of [4096, 4047, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- 1155 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 15 times 0, 1, 54 times 0, 1, 151 times 0, 1, 337 times 0, 1, 589 times 0) [i] based on linear OA(1652, 4099, F16, 19) (dual of [4099, 4047, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1660, 5262, F16, 19) (dual of [5262, 5202, 20]-code), using
- discarding factors / shortening the dual code based on linear OOA(1660, 5262, F16, 2, 19) (dual of [(5262, 2), 10464, 20]-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.