Information on Result #674528
Linear OA(3146, 531454, F3, 19) (dual of [531454, 531308, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(31, 13, F3, 1) (dual of [13, 12, 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(3147, 531455, F3, 19) (dual of [531455, 531308, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3148, 531456, F3, 19) (dual of [531456, 531308, 20]-code) | [i] | ||
| 3 | Linear OA(3145, 531453, F3, 18) (dual of [531453, 531308, 19]-code) | [i] | Truncation | |
| 4 | Linear OOA(3146, 265727, F3, 2, 19) (dual of [(265727, 2), 531308, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3146, 177151, F3, 3, 19) (dual of [(177151, 3), 531307, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(3146, 132863, F3, 4, 19) (dual of [(132863, 4), 531306, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(3146, 106290, F3, 5, 19) (dual of [(106290, 5), 531304, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(3146, 59050, F3, 19, 19) (dual of [(59050, 19), 1121804, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |