Information on Result #1743544
Digital (31, 52, 1075)-net over F49, using net defined by OOA based on linear OOA(4952, 1075, F49, 27, 21) (dual of [(1075, 27), 28973, 22]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4952, 4301, F49, 3, 21) (dual of [(4301, 3), 12851, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4952, 4302, F49, 3, 21) (dual of [(4302, 3), 12854, 22]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4952, 4302, F49, 21) (dual of [4302, 4250, 22]-code), using
- 1888 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 8 times 0, 1, 23 times 0, 1, 62 times 0, 1, 154 times 0, 1, 330 times 0, 1, 556 times 0, 1, 745 times 0) [i] based on linear OA(4941, 2403, F49, 21) (dual of [2403, 2362, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(4941, 2401, F49, 21) (dual of [2401, 2360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4939, 2401, F49, 20) (dual of [2401, 2362, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- 1888 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 8 times 0, 1, 23 times 0, 1, 62 times 0, 1, 154 times 0, 1, 330 times 0, 1, 556 times 0, 1, 745 times 0) [i] based on linear OA(4941, 2403, F49, 21) (dual of [2403, 2362, 22]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4952, 4302, F49, 21) (dual of [4302, 4250, 22]-code), using
- discarding factors / shortening the dual code based on linear OOA(4952, 4302, F49, 3, 21) (dual of [(4302, 3), 12854, 22]-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.