Information on Result #1523763
Linear OOA(3140, 26777, F3, 3, 20) (dual of [(26777, 3), 80191, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3140, 26777, F3, 2, 20) (dual of [(26777, 2), 53414, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3140, 29544, F3, 2, 20) (dual of [(29544, 2), 58948, 21]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3138, 29543, F3, 2, 20) (dual of [(29543, 2), 58948, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3138, 59086, F3, 20) (dual of [59086, 58948, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3137, 59085, F3, 20) (dual of [59085, 58948, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3137, 59085, F3, 20) (dual of [59085, 58948, 21]-code), using
- OOA 2-folding [i] based on linear OA(3138, 59086, F3, 20) (dual of [59086, 58948, 21]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3138, 29543, F3, 2, 20) (dual of [(29543, 2), 58948, 21]-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(3140, 13388, F3, 5, 20) (dual of [(13388, 5), 66800, 21]-NRT-code) | [i] | OOA Folding | |