Information on Result #2479333
Linear OOA(2148, 1031, F2, 2, 26) (dual of [(1031, 2), 1914, 27]-NRT-code), using 21 times duplication based on linear OOA(2147, 1031, F2, 2, 26) (dual of [(1031, 2), 1915, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2145, 1030, F2, 2, 26) (dual of [(1030, 2), 1915, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2145, 2060, F2, 26) (dual of [2060, 1915, 27]-code), using
- strength reduction [i] based on linear OA(2145, 2060, F2, 27) (dual of [2060, 1915, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(21, 12, F2, 1) (dual of [12, 11, 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(26) ⊂ Ce(24) [i] based on
- strength reduction [i] based on linear OA(2145, 2060, F2, 27) (dual of [2060, 1915, 28]-code), using
- OOA 2-folding [i] based on linear OA(2145, 2060, F2, 26) (dual of [2060, 1915, 27]-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(2148, 735, F2, 3, 26) (dual of [(735, 3), 2057, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2148, 735, F2, 4, 26) (dual of [(735, 4), 2792, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(2148, 735, F2, 5, 26) (dual of [(735, 5), 3527, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(2148, 735, F2, 6, 26) (dual of [(735, 6), 4262, 27]-NRT-code) | [i] | ||
| 5 | Linear OOA(2148, 735, F2, 7, 26) (dual of [(735, 7), 4997, 27]-NRT-code) | [i] | ||
| 6 | Linear OOA(2148, 735, F2, 8, 26) (dual of [(735, 8), 5732, 27]-NRT-code) | [i] | ||
| 7 | Digital (122, 148, 735)-net over F2 | [i] | ||