Information on Result #961829
Linear OOA(4114, 21851, F4, 3, 19) (dual of [(21851, 3), 65439, 20]-NRT-code), using OOA 3-folding based on linear OA(4114, 65553, F4, 19) (dual of [65553, 65439, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4114, 65554, F4, 19) (dual of [65554, 65440, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(4113, 65537, F4, 19) (dual of [65537, 65424, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(41, 17, F4, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
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(4115, 21851, F4, 3, 19) (dual of [(21851, 3), 65438, 20]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(4126, 21865, F4, 3, 19) (dual of [(21865, 3), 65469, 20]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |