Information on Result #674561
Linear OA(3137, 531469, F3, 17) (dual of [531469, 531332, 18]-code), using construction X applied to Ce(16) ⊂ Ce(13) based on
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(34, 28, F3, 2) (dual of [28, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 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(3138, 531470, F3, 17) (dual of [531470, 531332, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3137, 265734, F3, 2, 17) (dual of [(265734, 2), 531331, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3137, 177156, F3, 3, 17) (dual of [(177156, 3), 531331, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(3137, 132867, F3, 4, 17) (dual of [(132867, 4), 531331, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(3137, 106293, F3, 5, 17) (dual of [(106293, 5), 531328, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(3137, 66433, F3, 17, 17) (dual of [(66433, 17), 1129224, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |