Information on Result #674870
Linear OA(3122, 59060, F3, 19) (dual of [59060, 58938, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- linear OA(3121, 59049, F3, 19) (dual of [59049, 58928, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 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(3123, 59061, F3, 19) (dual of [59061, 58938, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3124, 59062, F3, 19) (dual of [59062, 58938, 20]-code) | [i] | ||
| 3 | Linear OA(3121, 59059, F3, 18) (dual of [59059, 58938, 19]-code) | [i] | Truncation | |
| 4 | Linear OOA(3122, 29530, F3, 2, 19) (dual of [(29530, 2), 58938, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3122, 19686, F3, 3, 19) (dual of [(19686, 3), 58936, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(3122, 14765, F3, 4, 19) (dual of [(14765, 4), 58938, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(3122, 11812, F3, 5, 19) (dual of [(11812, 5), 58938, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(3122, 6562, F3, 19, 19) (dual of [(6562, 19), 124556, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |