Information on Result #1591068
Linear OOA(2130, 1249, F2, 4, 21) (dual of [(1249, 4), 4866, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2130, 1249, F2, 3, 21) (dual of [(1249, 3), 3617, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2130, 1376, F2, 3, 21) (dual of [(1376, 3), 3998, 22]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2128, 1376, F2, 3, 21) (dual of [(1376, 3), 4000, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2128, 4128, F2, 21) (dual of [4128, 4000, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2127, 4127, F2, 21) (dual of [4127, 4000, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2121, 4097, F2, 21) (dual of [4097, 3976, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(297, 4097, F2, 17) (dual of [4097, 4000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2127, 4127, F2, 21) (dual of [4127, 4000, 22]-code), using
- OOA 3-folding [i] based on linear OA(2128, 4128, F2, 21) (dual of [4128, 4000, 22]-code), using
- 22 times duplication [i] based on linear OOA(2128, 1376, F2, 3, 21) (dual of [(1376, 3), 4000, 22]-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(2130, 624, F2, 7, 21) (dual of [(624, 7), 4238, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2130, 624, F2, 8, 21) (dual of [(624, 8), 4862, 22]-NRT-code) | [i] | ||