Information on Result #1691610
Linear OOA(2184, 550, F2, 8, 31) (dual of [(550, 8), 4216, 32]-NRT-code), using OOA 2-folding based on linear OOA(2184, 1100, F2, 4, 31) (dual of [(1100, 4), 4216, 32]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2184, 1100, F2, 3, 31) (dual of [(1100, 3), 3116, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2184, 1370, F2, 3, 31) (dual of [(1370, 3), 3926, 32]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2183, 1370, F2, 3, 31) (dual of [(1370, 3), 3927, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2183, 4110, F2, 31) (dual of [4110, 3927, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2182, 4109, F2, 31) (dual of [4109, 3927, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2169, 4096, F2, 29) (dual of [4096, 3927, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(30) ⊂ Ce(28) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2182, 4109, F2, 31) (dual of [4109, 3927, 32]-code), using
- OOA 3-folding [i] based on linear OA(2183, 4110, F2, 31) (dual of [4110, 3927, 32]-code), using
- 21 times duplication [i] based on linear OOA(2183, 1370, F2, 3, 31) (dual of [(1370, 3), 3927, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2184, 1370, F2, 3, 31) (dual of [(1370, 3), 3926, 32]-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.