Information on Result #1522812
Linear OOA(3122, 4314, F3, 3, 21) (dual of [(4314, 3), 12820, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3122, 4314, F3, 21) (dual of [4314, 4192, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3122, 6602, F3, 21) (dual of [6602, 6480, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3121, 6601, F3, 21) (dual of [6601, 6480, 22]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(381, 6561, F3, 16) (dual of [6561, 6480, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(38, 40, F3, 4) (dual of [40, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3121, 6601, F3, 21) (dual of [6601, 6480, 22]-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(3122, 2157, F3, 5, 21) (dual of [(2157, 5), 10663, 22]-NRT-code) | [i] | OOA Folding | |