Information on Result #703718
Linear OA(3243, 274, F3, 134) (dual of [274, 31, 135]-code), using construction XX applied to C1 = C([233,120]), C2 = C([0,124]), C3 = C1 + C2 = C([0,120]), and C∩ = C1 ∩ C2 = C([233,124]) based on
- linear OA(3221, 242, F3, 130) (dual of [242, 21, 131]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−9,−8,…,120}, and designed minimum distance d ≥ |I|+1 = 131 [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(3211, 242, F3, 121) (dual of [242, 31, 122]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,120], and designed minimum distance d ≥ |I|+1 = 122 [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(34, 10, F3, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), 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(3244, 275, F3, 134) (dual of [275, 31, 135]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3245, 276, F3, 134) (dual of [276, 31, 135]-code) | [i] | ||
| 3 | Linear OA(3246, 277, F3, 134) (dual of [277, 31, 135]-code) | [i] | ||
| 4 | Linear OA(3247, 278, F3, 134) (dual of [278, 31, 135]-code) | [i] | ||
| 5 | Linear OA(3241, 272, F3, 132) (dual of [272, 31, 133]-code) | [i] | Truncation | |
| 6 | Linear OOA(3243, 137, F3, 2, 134) (dual of [(137, 2), 31, 135]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3243, 91, F3, 3, 134) (dual of [(91, 3), 30, 135]-NRT-code) | [i] | ||