Information on Result #1525601
Linear OOA(3170, 3285, F3, 3, 32) (dual of [(3285, 3), 9685, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3170, 3285, F3, 2, 32) (dual of [(3285, 2), 6400, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3170, 6570, F3, 32) (dual of [6570, 6400, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3169, 6569, F3, 32) (dual of [6569, 6400, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 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
- 1 times code embedding in larger space [i] based on linear OA(3169, 6569, F3, 32) (dual of [6569, 6400, 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(3170, 1642, F3, 5, 32) (dual of [(1642, 5), 8040, 33]-NRT-code) | [i] | OOA Folding | |