Information on Result #1743136
Digital (19, 31, 2969)-net over F49, using net defined by OOA based on linear OOA(4931, 2969, F49, 15, 12) (dual of [(2969, 15), 44504, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(4931, 5939, F49, 3, 12) (dual of [(5939, 3), 17786, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4931, 5939, F49, 12) (dual of [5939, 5908, 13]-code), using
- 3528 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 41 times 0, 1, 162 times 0, 1, 496 times 0, 1, 1080 times 0, 1, 1737 times 0) [i] based on linear OA(4923, 2403, F49, 12) (dual of [2403, 2380, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4921, 2401, F49, 11) (dual of [2401, 2380, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- 3528 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 41 times 0, 1, 162 times 0, 1, 496 times 0, 1, 1080 times 0, 1, 1737 times 0) [i] based on linear OA(4923, 2403, F49, 12) (dual of [2403, 2380, 13]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4931, 5939, F49, 12) (dual of [5939, 5908, 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.