Information on Result #1643213
Linear OOA(3123, 22659, F3, 5, 18) (dual of [(22659, 5), 113172, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3123, 22659, F3, 2, 18) (dual of [(22659, 2), 45195, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3123, 29536, F3, 2, 18) (dual of [(29536, 2), 58949, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3123, 59072, F3, 18) (dual of [59072, 58949, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3122, 59071, F3, 18) (dual of [59071, 58949, 19]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(15) [i] 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(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(321, 22, F3, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,3)), using
- dual of repetition code with length 22 [i]
- linear OA(31, 22, F3, 1) (dual of [22, 21, 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
- construction X4 applied to Ce(18) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3122, 59071, F3, 18) (dual of [59071, 58949, 19]-code), using
- OOA 2-folding [i] based on linear OA(3123, 59072, F3, 18) (dual of [59072, 58949, 19]-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(3123, 11329, F3, 25, 18) (dual of [(11329, 25), 283102, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |