Information on Result #703888
Linear OA(377, 377, F3, 20) (dual of [377, 300, 21]-code), using construction XX applied to C1 = C([164,182]), C2 = C([166,183]), C3 = C1 + C2 = C([166,182]), and C∩ = C1 ∩ C2 = C([164,183]) based on
- linear OA(370, 364, F3, 19) (dual of [364, 294, 20]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {164,165,…,182}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(370, 364, F3, 18) (dual of [364, 294, 19]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {166,167,…,183}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(376, 364, F3, 20) (dual of [364, 288, 21]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {164,165,…,183}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(364, 364, F3, 17) (dual of [364, 300, 18]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {166,167,…,182}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-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 OOA(377, 375, F3, 2, 20) (dual of [(375, 2), 673, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(377, 375, F3, 3, 20) (dual of [(375, 3), 1048, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(377, 375, F3, 4, 20) (dual of [(375, 4), 1423, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(377, 375, F3, 5, 20) (dual of [(375, 5), 1798, 21]-NRT-code) | [i] | ||
| 5 | Digital (57, 77, 375)-net over F3 | [i] | ||
| 6 | Linear OA(378, 385, F3, 20) (dual of [385, 307, 21]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OOA(377, 188, F3, 2, 20) (dual of [(188, 2), 299, 21]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(377, 125, F3, 3, 20) (dual of [(125, 3), 298, 21]-NRT-code) | [i] | ||