Information on Result #675697
Linear OA(3118, 6585, F3, 21) (dual of [6585, 6467, 22]-code), using construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(16) 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(397, 6561, F3, 19) (dual of [6561, 6464, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(31, 20, F3, 1) (dual of [20, 19, 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
- linear OA(31, 4, F3, 1) (dual of [4, 3, 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 (see above)
Mode: Constructive and 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(3118, 3420, F3, 2, 21) (dual of [(3420, 2), 6722, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3118, 3420, F3, 3, 21) (dual of [(3420, 3), 10142, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(3118, 3420, F3, 4, 21) (dual of [(3420, 4), 13562, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(3118, 3420, F3, 5, 21) (dual of [(3420, 5), 16982, 22]-NRT-code) | [i] | ||
| 5 | Digital (97, 118, 3420)-net over F3 | [i] | ||
| 6 | Linear OOA(3118, 3292, F3, 2, 21) (dual of [(3292, 2), 6466, 22]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3118, 2195, F3, 3, 21) (dual of [(2195, 3), 6467, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(3118, 1646, F3, 4, 21) (dual of [(1646, 4), 6466, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(3118, 1317, F3, 5, 21) (dual of [(1317, 5), 6467, 22]-NRT-code) | [i] | ||