Information on Result #1675275
Linear OOA(2245, 655, F2, 7, 41) (dual of [(655, 7), 4340, 42]-NRT-code), using OOA 2-folding based on linear OOA(2245, 1310, F2, 4, 41) (dual of [(1310, 4), 4995, 42]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2245, 1310, F2, 3, 41) (dual of [(1310, 3), 3685, 42]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2245, 1370, F2, 3, 41) (dual of [(1370, 3), 3865, 42]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2243, 1370, F2, 3, 41) (dual of [(1370, 3), 3867, 42]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2243, 4110, F2, 41) (dual of [4110, 3867, 42]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2242, 4109, F2, 41) (dual of [4109, 3867, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(38) [i] based on
- linear OA(2241, 4096, F2, 41) (dual of [4096, 3855, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2229, 4096, F2, 39) (dual of [4096, 3867, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(40) ⊂ Ce(38) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2242, 4109, F2, 41) (dual of [4109, 3867, 42]-code), using
- OOA 3-folding [i] based on linear OA(2243, 4110, F2, 41) (dual of [4110, 3867, 42]-code), using
- 22 times duplication [i] based on linear OOA(2243, 1370, F2, 3, 41) (dual of [(1370, 3), 3867, 42]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2245, 1370, F2, 3, 41) (dual of [(1370, 3), 3865, 42]-NRT-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.