Information on Result #1593652
Linear OOA(2178, 686, F2, 4, 33) (dual of [(686, 4), 2566, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2178, 686, F2, 3, 33) (dual of [(686, 3), 1880, 34]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2178, 2058, F2, 33) (dual of [2058, 1880, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2178, 2060, F2, 33) (dual of [2060, 1882, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(2177, 2048, F2, 33) (dual of [2048, 1871, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(32) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(2178, 2060, F2, 33) (dual of [2060, 1882, 34]-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(2178, 343, F2, 7, 33) (dual of [(343, 7), 2223, 34]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2178, 343, F2, 8, 33) (dual of [(343, 8), 2566, 34]-NRT-code) | [i] | ||