Information on Result #703721
Linear OA(3240, 270, F3, 133) (dual of [270, 30, 134]-code), using construction XX applied to C1 = C([233,121]), C2 = C([0,124]), C3 = C1 + C2 = C([0,121]), and C∩ = C1 ∩ C2 = C([233,124]) based on
- linear OA(3222, 242, F3, 131) (dual of [242, 20, 132]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−9,−8,…,121}, and designed minimum distance d ≥ |I|+1 = 132 [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(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 = {−9,−8,…,124}, and designed minimum distance d ≥ |I|+1 = 135 [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(312, 22, F3, 8) (dual of [22, 10, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(312, 24, F3, 8) (dual of [24, 12, 9]-code), using
- extended quadratic residue code Qe(24,3) [i]
- discarding factors / shortening the dual code based on linear OA(312, 24, F3, 8) (dual of [24, 12, 9]-code), 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(3239, 269, F3, 132) (dual of [269, 30, 133]-code) | [i] | Truncation | |
| 2 | Linear OOA(3240, 135, F3, 2, 133) (dual of [(135, 2), 30, 134]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3240, 90, F3, 3, 133) (dual of [(90, 3), 30, 134]-NRT-code) | [i] | ||
| 4 | Linear OOA(3240, 54, F3, 5, 133) (dual of [(54, 5), 30, 134]-NRT-code) | [i] | ||