Information on Result #703757
Linear OA(3237, 258, F3, 136) (dual of [258, 21, 137]-code), using construction XX applied to C1 = C([239,130]), C2 = C([1,133]), C3 = C1 + C2 = C([1,130]), and C∩ = C1 ∩ C2 = C([239,133]) based on
- linear OA(3227, 242, F3, 134) (dual of [242, 15, 135]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,130}, and designed minimum distance d ≥ |I|+1 = 135 [i]
- linear OA(3226, 242, F3, 133) (dual of [242, 16, 134]-code), using the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,133], and designed minimum distance d ≥ |I|+1 = 134 [i]
- linear OA(3232, 242, F3, 137) (dual of [242, 10, 138]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,133}, and designed minimum distance d ≥ |I|+1 = 138 [i]
- linear OA(3221, 242, F3, 130) (dual of [242, 21, 131]-code), using the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,130], and designed minimum distance d ≥ |I|+1 = 131 [i]
- linear OA(34, 10, F3, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
- 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
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(3236, 257, F3, 135) (dual of [257, 21, 136]-code) | [i] | Truncation | |
| 2 | Linear OA(3235, 256, F3, 134) (dual of [256, 21, 135]-code) | [i] | ||
| 3 | Linear OOA(3237, 129, F3, 2, 136) (dual of [(129, 2), 21, 137]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3237, 86, F3, 3, 136) (dual of [(86, 3), 21, 137]-NRT-code) | [i] | ||