Information on Result #1643931
Linear OOA(3137, 63202, F3, 5, 18) (dual of [(63202, 5), 315873, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3137, 63202, F3, 2, 18) (dual of [(63202, 2), 126267, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3137, 88587, F3, 2, 18) (dual of [(88587, 2), 177037, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3135, 88586, F3, 2, 18) (dual of [(88586, 2), 177037, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3135, 177172, F3, 18) (dual of [177172, 177037, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3134, 177171, F3, 18) (dual of [177171, 177037, 19]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(323, 24, F3, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
- dual of repetition code with length 24 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 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(3134, 177171, F3, 18) (dual of [177171, 177037, 19]-code), using
- OOA 2-folding [i] based on linear OA(3135, 177172, F3, 18) (dual of [177172, 177037, 19]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3135, 88586, F3, 2, 18) (dual of [(88586, 2), 177037, 19]-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(3137, 31600, F3, 25, 18) (dual of [(31600, 25), 789863, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |