Information on Result #675707
Linear OA(3102, 6585, F3, 18) (dual of [6585, 6483, 19]-code), using construction XX applied to Ce(18) ⊂ Ce(15) ⊂ Ce(13) based on
- 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(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(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(3102, 3479, F3, 2, 18) (dual of [(3479, 2), 6856, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3102, 3479, F3, 3, 18) (dual of [(3479, 3), 10335, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(3102, 3479, F3, 4, 18) (dual of [(3479, 4), 13814, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(3102, 3479, F3, 5, 18) (dual of [(3479, 5), 17293, 19]-NRT-code) | [i] | ||
| 5 | Digital (84, 102, 3479)-net over F3 | [i] | ||
| 6 | Linear OOA(3102, 3292, F3, 2, 18) (dual of [(3292, 2), 6482, 19]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3102, 2195, F3, 3, 18) (dual of [(2195, 3), 6483, 19]-NRT-code) | [i] | ||
| 8 | Linear OOA(3102, 1646, F3, 4, 18) (dual of [(1646, 4), 6482, 19]-NRT-code) | [i] | ||
| 9 | Linear OOA(3102, 1317, F3, 5, 18) (dual of [(1317, 5), 6483, 19]-NRT-code) | [i] | ||