Information on Result #1681871
Linear OOA(2148, 735, F2, 7, 26) (dual of [(735, 7), 4997, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2148, 735, F2, 2, 26) (dual of [(735, 2), 1322, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2148, 1031, F2, 2, 26) (dual of [(1031, 2), 1914, 27]-NRT-code), using
- 21 times duplication [i] 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
- 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
- 21 times duplication [i] based on linear OOA(2147, 1031, F2, 2, 26) (dual of [(1031, 2), 1915, 27]-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(2148, 367, F2, 35, 26) (dual of [(367, 35), 12697, 27]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |