Information on Result #1635383
Linear OOA(2193, 1381, F2, 5, 31) (dual of [(1381, 5), 6712, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2193, 1381, F2, 3, 31) (dual of [(1381, 3), 3950, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2193, 4143, F2, 31) (dual of [4143, 3950, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2193, 4144, F2, 31) (dual of [4144, 3951, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [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(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(2193, 4144, F2, 31) (dual of [4144, 3951, 32]-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(2194, 1381, F2, 5, 31) (dual of [(1381, 5), 6711, 32]-NRT-code) | [i] | OOA Duplication | |