Information on Result #2480321
Linear OOA(2245, 2074, F2, 2, 38) (dual of [(2074, 2), 3903, 39]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(2241, 2072, F2, 2, 38) (dual of [(2072, 2), 3903, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2241, 4144, F2, 38) (dual of [4144, 3903, 39]-code), using
- strength reduction [i] based on linear OA(2241, 4144, F2, 39) (dual of [4144, 3903, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(32) [i] based on
- 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(2193, 4096, F2, 33) (dual of [4096, 3903, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(38) ⊂ Ce(32) [i] based on
- strength reduction [i] based on linear OA(2241, 4144, F2, 39) (dual of [4144, 3903, 40]-code), using
Mode: Constructive and 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(2246, 2074, F2, 2, 38) (dual of [(2074, 2), 3902, 39]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2245, 1660, F2, 3, 38) (dual of [(1660, 3), 4735, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2245, 1660, F2, 4, 38) (dual of [(1660, 4), 6395, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(2245, 1660, F2, 5, 38) (dual of [(1660, 5), 8055, 39]-NRT-code) | [i] | ||
| 5 | Linear OOA(2245, 1660, F2, 6, 38) (dual of [(1660, 6), 9715, 39]-NRT-code) | [i] | ||
| 6 | Linear OOA(2245, 1660, F2, 7, 38) (dual of [(1660, 7), 11375, 39]-NRT-code) | [i] | ||
| 7 | Linear OOA(2245, 1660, F2, 8, 38) (dual of [(1660, 8), 13035, 39]-NRT-code) | [i] | ||
| 8 | Digital (207, 245, 1660)-net over F2 | [i] | ||