Information on Result #1593794
Linear OOA(2180, 886, F2, 4, 31) (dual of [(886, 4), 3364, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2180, 886, F2, 2, 31) (dual of [(886, 2), 1592, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2180, 1047, F2, 2, 31) (dual of [(1047, 2), 1914, 32]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2179, 1047, F2, 2, 31) (dual of [(1047, 2), 1915, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2179, 2094, F2, 31) (dual of [2094, 1915, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2133, 2048, F2, 25) (dual of [2048, 1915, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(213, 46, F2, 5) (dual of [46, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- OOA 2-folding [i] based on linear OA(2179, 2094, F2, 31) (dual of [2094, 1915, 32]-code), using
- 21 times duplication [i] based on linear OOA(2179, 1047, F2, 2, 31) (dual of [(1047, 2), 1915, 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2180, 443, F2, 7, 31) (dual of [(443, 7), 2921, 32]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2180, 443, F2, 8, 31) (dual of [(443, 8), 3364, 32]-NRT-code) | [i] | ||