Information on Result #675185
Linear OA(3153, 19718, F3, 25) (dual of [19718, 19565, 26]-code), using construction X applied to Ce(24) ⊂ Ce(19) based on
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(38, 35, F3, 4) (dual of [35, 27, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3154, 19719, F3, 25) (dual of [19719, 19565, 26]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3152, 19717, F3, 24) (dual of [19717, 19565, 25]-code) | [i] | Truncation | |
| 3 | Linear OOA(3153, 9859, F3, 2, 25) (dual of [(9859, 2), 19565, 26]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3153, 6572, F3, 3, 25) (dual of [(6572, 3), 19563, 26]-NRT-code) | [i] | ||
| 5 | Linear OOA(3153, 4929, F3, 4, 25) (dual of [(4929, 4), 19563, 26]-NRT-code) | [i] | ||
| 6 | Linear OOA(3153, 3943, F3, 5, 25) (dual of [(3943, 5), 19562, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(3153, 1643, F3, 25, 25) (dual of [(1643, 25), 40922, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |