Information on Result #1702685
Linear OOA(2206, 1488, F2, 8, 32) (dual of [(1488, 8), 11698, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2206, 1488, F2, 2, 32) (dual of [(1488, 2), 2770, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2206, 2072, F2, 2, 32) (dual of [(2072, 2), 3938, 33]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2205, 2072, F2, 2, 32) (dual of [(2072, 2), 3939, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2205, 4144, F2, 32) (dual of [4144, 3939, 33]-code), using
- strength reduction [i] based on linear OA(2205, 4144, F2, 33) (dual of [4144, 3939, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- 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(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(32) ⊂ Ce(26) [i] based on
- strength reduction [i] based on linear OA(2205, 4144, F2, 33) (dual of [4144, 3939, 34]-code), using
- OOA 2-folding [i] based on linear OA(2205, 4144, F2, 32) (dual of [4144, 3939, 33]-code), using
- 21 times duplication [i] based on linear OOA(2205, 2072, F2, 2, 32) (dual of [(2072, 2), 3939, 33]-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(2206, 743, F2, 40, 32) (dual of [(743, 40), 29514, 33]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |