Information on Result #1702323
Linear OOA(2201, 1284, F2, 8, 33) (dual of [(1284, 8), 10071, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2201, 1284, F2, 3, 33) (dual of [(1284, 3), 3651, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2201, 1376, F2, 3, 33) (dual of [(1376, 3), 3927, 34]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2200, 1376, F2, 3, 33) (dual of [(1376, 3), 3928, 34]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2200, 4128, F2, 33) (dual of [4128, 3928, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2199, 4127, F2, 33) (dual of [4127, 3928, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2193, 4097, F2, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2169, 4097, F2, 29) (dual of [4097, 3928, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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([0,16]) ⊂ C([0,14]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2199, 4127, F2, 33) (dual of [4127, 3928, 34]-code), using
- OOA 3-folding [i] based on linear OA(2200, 4128, F2, 33) (dual of [4128, 3928, 34]-code), using
- 21 times duplication [i] based on linear OOA(2200, 1376, F2, 3, 33) (dual of [(1376, 3), 3928, 34]-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(2201, 641, F2, 40, 33) (dual of [(641, 40), 25439, 34]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |