Information on Result #676137
Linear OA(3241, 2197, F3, 52) (dual of [2197, 1956, 53]-code), using construction XX applied to Ce(51) ⊂ Ce(49) ⊂ Ce(48) based on
- linear OA(3239, 2187, F3, 52) (dual of [2187, 1948, 53]-code), using an extension Ce(51) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3232, 2187, F3, 50) (dual of [2187, 1955, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(3225, 2187, F3, 49) (dual of [2187, 1962, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(3241, 1854, F3, 2, 52) (dual of [(1854, 2), 3467, 53]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3241, 1854, F3, 3, 52) (dual of [(1854, 3), 5321, 53]-NRT-code) | [i] | ||
| 3 | Linear OOA(3241, 1854, F3, 4, 52) (dual of [(1854, 4), 7175, 53]-NRT-code) | [i] | ||
| 4 | Linear OOA(3241, 1854, F3, 5, 52) (dual of [(1854, 5), 9029, 53]-NRT-code) | [i] | ||
| 5 | Digital (189, 241, 1854)-net over F3 | [i] | ||
| 6 | Linear OOA(3241, 1098, F3, 2, 52) (dual of [(1098, 2), 1955, 53]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3241, 732, F3, 3, 52) (dual of [(732, 3), 1955, 53]-NRT-code) | [i] | ||
| 8 | Linear OOA(3241, 549, F3, 4, 52) (dual of [(549, 4), 1955, 53]-NRT-code) | [i] | ||