Information on Result #677158
Linear OA(3230, 251, F3, 134) (dual of [251, 21, 135]-code), using construction X applied to Ce(133) ⊂ Ce(130) based on
- linear OA(3227, 243, F3, 134) (dual of [243, 16, 135]-code), using an extension Ce(133) of 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(3222, 243, F3, 131) (dual of [243, 21, 132]-code), using an extension Ce(130) of 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(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(3230, 251, F3, 133) (dual of [251, 21, 134]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3230, 251, F3, 132) (dual of [251, 21, 133]-code) | [i] | ||
| 3 | Linear OA(3231, 252, F3, 134) (dual of [252, 21, 135]-code) | [i] | Code Embedding in Larger Space | |
| 4 | Linear OA(3232, 253, F3, 134) (dual of [253, 21, 135]-code) | [i] | ||
| 5 | Linear OA(3233, 254, F3, 134) (dual of [254, 21, 135]-code) | [i] | ||
| 6 | Linear OA(3234, 255, F3, 134) (dual of [255, 21, 135]-code) | [i] | ||
| 7 | Linear OA(3229, 250, F3, 133) (dual of [250, 21, 134]-code) | [i] | Truncation | |
| 8 | Linear OOA(3230, 125, F3, 2, 134) (dual of [(125, 2), 20, 135]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(3230, 83, F3, 3, 134) (dual of [(83, 3), 19, 135]-NRT-code) | [i] | ||
| 10 | Linear OOA(3230, 50, F3, 5, 134) (dual of [(50, 5), 20, 135]-NRT-code) | [i] | ||