Information on Result #703714
Linear OA(3226, 256, F3, 127) (dual of [256, 30, 128]-code), using construction XX applied to C1 = C([239,121]), C2 = C([0,124]), C3 = C1 + C2 = C([0,121]), and C∩ = C1 ∩ C2 = C([239,124]) based on
- linear OA(3217, 242, F3, 125) (dual of [242, 25, 126]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,121}, and designed minimum distance d ≥ |I|+1 = 126 [i]
- linear OA(3217, 242, F3, 125) (dual of [242, 25, 126]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,124], and designed minimum distance d ≥ |I|+1 = 126 [i]
- linear OA(3222, 242, F3, 128) (dual of [242, 20, 129]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,124}, and designed minimum distance d ≥ |I|+1 = 129 [i]
- linear OA(3212, 242, F3, 122) (dual of [242, 30, 123]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,121], and designed minimum distance d ≥ |I|+1 = 123 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 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(33, 8, F3, 2) (dual of [8, 5, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3225, 255, F3, 126) (dual of [255, 30, 127]-code) | [i] | Truncation | |
| 2 | Linear OOA(3226, 128, F3, 2, 127) (dual of [(128, 2), 30, 128]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3226, 85, F3, 3, 127) (dual of [(85, 3), 29, 128]-NRT-code) | [i] | ||
| 4 | Linear OOA(3226, 51, F3, 5, 127) (dual of [(51, 5), 29, 128]-NRT-code) | [i] | ||