Information on Result #681982
Linear OA(451, 78, F4, 26) (dual of [78, 27, 27]-code), using construction X applied to C([0,77]) ⊂ C([1,62]) based on
- linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using contraction [i] based on linear OA(4170, 189, F4, 80) (dual of [189, 19, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,77], and minimum distance d ≥ |{−2,−1,…,77}|+1 = 81 (BCH-bound) [i]
- linear OA(436, 63, F4, 20) (dual of [63, 27, 21]-code), using contraction [i] based on linear OA(4162, 189, F4, 62) (dual of [189, 27, 63]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(47, 15, F4, 5) (dual of [15, 8, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 16, F4, 5) (dual of [16, 9, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 15 = 42−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(47, 16, F4, 5) (dual of [16, 9, 6]-code), using
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(451, 78, F4, 25) (dual of [78, 27, 26]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(451, 78, F4, 24) (dual of [78, 27, 25]-code) | [i] | ||
| 3 | Linear OOA(451, 26, F4, 3, 26) (dual of [(26, 3), 27, 27]-NRT-code) | [i] | OOA Folding | |