Information on Result #1609712
Linear OOA(3213, 19687, F3, 4, 32) (dual of [(19687, 4), 78535, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3213, 19687, F3, 3, 32) (dual of [(19687, 3), 58848, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3213, 59061, F3, 32) (dual of [59061, 58848, 33]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3211, 59059, F3, 32) (dual of [59059, 58848, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3211, 59049, F3, 32) (dual of [59049, 58838, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(31) ⊂ Ce(30) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3211, 59059, F3, 32) (dual of [59059, 58848, 33]-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(3214, 19687, F3, 4, 32) (dual of [(19687, 4), 78534, 33]-NRT-code) | [i] | OOA Duplication | |