Information on Result #1580220
Linear OOA(3219, 1769, F3, 4, 41) (dual of [(1769, 4), 6857, 42]-NRT-code), using OOA 2-folding based on linear OOA(3219, 3538, F3, 2, 41) (dual of [(3538, 2), 6857, 42]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3219, 3539, F3, 2, 41) (dual of [(3539, 2), 6859, 42]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3219, 3539, F3, 41) (dual of [3539, 3320, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(3219, 6572, F3, 41) (dual of [6572, 6353, 42]-code), using
- construction XX applied to Ce(40) ⊂ Ce(39) ⊂ Ce(37) [i] based on
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(40) ⊂ Ce(39) ⊂ Ce(37) [i] based on
- discarding factors / shortening the dual code based on linear OA(3219, 6572, F3, 41) (dual of [6572, 6353, 42]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3219, 3539, F3, 41) (dual of [3539, 3320, 42]-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.