Information on Result #1603248
Linear OOA(3114, 19820, F3, 4, 17) (dual of [(19820, 4), 79166, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3114, 19820, F3, 2, 17) (dual of [(19820, 2), 39526, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3114, 29531, F3, 2, 17) (dual of [(29531, 2), 58948, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3112, 29530, F3, 2, 17) (dual of [(29530, 2), 58948, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3112, 59060, F3, 17) (dual of [59060, 58948, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3111, 59059, F3, 17) (dual of [59059, 58948, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 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(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 10, F3, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3111, 59059, F3, 17) (dual of [59059, 58948, 18]-code), using
- OOA 2-folding [i] based on linear OA(3112, 59060, F3, 17) (dual of [59060, 58948, 18]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3112, 29530, F3, 2, 17) (dual of [(29530, 2), 58948, 18]-NRT-code), using
Mode: 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 OOA(3114, 9909, F3, 20, 17) (dual of [(9909, 20), 198066, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |