Information on Result #1642610
Linear OOA(3110, 3291, F3, 5, 20) (dual of [(3291, 5), 16345, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3110, 3291, F3, 2, 20) (dual of [(3291, 2), 6472, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3110, 6582, F3, 20) (dual of [6582, 6472, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3110, 6583, F3, 20) (dual of [6583, 6473, 21]-code), using
- construction XX applied to Ce(19) ⊂ Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3105, 6561, F3, 20) (dual of [6561, 6456, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(389, 6561, F3, 17) (dual of [6561, 6472, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(34, 21, F3, 2) (dual of [21, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(19) ⊂ Ce(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3110, 6583, F3, 20) (dual of [6583, 6473, 21]-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(3110, 1645, F3, 25, 20) (dual of [(1645, 25), 41015, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |