Information on Result #709669
Linear OA(4258, 1056, F4, 70) (dual of [1056, 798, 71]-code), using construction XX applied to C1 = C([273,340]), C2 = C([281,342]), C3 = C1 + C2 = C([281,340]), and C∩ = C1 ∩ C2 = C([273,342]) based on
- linear OA(4240, 1023, F4, 68) (dual of [1023, 783, 69]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {273,274,…,340}, and designed minimum distance d ≥ |I|+1 = 69 [i]
- linear OA(4231, 1023, F4, 62) (dual of [1023, 792, 63]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {281,282,…,342}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(4246, 1023, F4, 70) (dual of [1023, 777, 71]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {273,274,…,342}, and designed minimum distance d ≥ |I|+1 = 71 [i]
- linear OA(4225, 1023, F4, 60) (dual of [1023, 798, 61]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {281,282,…,340}, and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(411, 26, F4, 7) (dual of [26, 15, 8]-code), using
- 4 times truncation [i] based on linear OA(415, 30, F4, 11) (dual of [30, 15, 12]-code), using
- extended quadratic residue code Qe(30,4) [i]
- 4 times truncation [i] based on linear OA(415, 30, F4, 11) (dual of [30, 15, 12]-code), using
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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
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 OA(4259, 1057, F4, 70) (dual of [1057, 798, 71]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4258, 528, F4, 2, 70) (dual of [(528, 2), 798, 71]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4258, 352, F4, 3, 70) (dual of [(352, 3), 798, 71]-NRT-code) | [i] | ||