Information on Result #1623340
Linear OOA(3241, 1116, F3, 5, 50) (dual of [(1116, 5), 5339, 51]-NRT-code), using OOA 2-folding based on linear OOA(3241, 2232, F3, 3, 50) (dual of [(2232, 3), 6455, 51]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3241, 2232, F3, 50) (dual of [2232, 1991, 51]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, 2244, F3, 50) (dual of [2244, 2003, 51]-code), using
- 41 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 9 times 0, 1, 13 times 0) [i] based on linear OA(3232, 2194, F3, 50) (dual of [2194, 1962, 51]-code), using
- construction X applied to Ce(49) ⊂ Ce(48) [i] based on
- linear OA(3232, 2187, F3, 50) (dual of [2187, 1955, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(3225, 2187, F3, 49) (dual of [2187, 1962, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(49) ⊂ Ce(48) [i] based on
- 41 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 9 times 0, 1, 13 times 0) [i] based on linear OA(3232, 2194, F3, 50) (dual of [2194, 1962, 51]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, 2244, F3, 50) (dual of [2244, 2003, 51]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.