Information on Result #703254
Linear OA(370, 262, F3, 20) (dual of [262, 192, 21]-code), using construction XX applied to C1 = C([103,120]), C2 = C([106,122]), C3 = C1 + C2 = C([106,120]), and C∩ = C1 ∩ C2 = C([103,122]) based on
- linear OA(360, 242, F3, 18) (dual of [242, 182, 19]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {103,104,…,120}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(356, 242, F3, 17) (dual of [242, 186, 18]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {106,107,…,122}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(366, 242, F3, 20) (dual of [242, 176, 21]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {103,104,…,122}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(350, 242, F3, 15) (dual of [242, 192, 16]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {106,107,…,120}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [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
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(370, 240, F3, 2, 20) (dual of [(240, 2), 410, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(370, 240, F3, 3, 20) (dual of [(240, 3), 650, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(370, 240, F3, 4, 20) (dual of [(240, 4), 890, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(370, 240, F3, 5, 20) (dual of [(240, 5), 1130, 21]-NRT-code) | [i] | ||
| 5 | Digital (50, 70, 240)-net over F3 | [i] | ||
| 6 | Linear OOA(370, 131, F3, 2, 20) (dual of [(131, 2), 192, 21]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(370, 87, F3, 3, 20) (dual of [(87, 3), 191, 21]-NRT-code) | [i] | ||