Information on Result #675881
Linear OA(3240, 2195, F3, 52) (dual of [2195, 1955, 53]-code), using construction X applied to Ce(51) ⊂ Ce(49) 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(31, 8, F3, 1) (dual of [8, 7, 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
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 OA(3239, 2194, F3, 51) (dual of [2194, 1955, 52]-code) | [i] | Truncation | |
| 2 | Linear OOA(3240, 1813, F3, 2, 52) (dual of [(1813, 2), 3386, 53]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3240, 1813, F3, 3, 52) (dual of [(1813, 3), 5199, 53]-NRT-code) | [i] | ||
| 4 | Linear OOA(3240, 1813, F3, 4, 52) (dual of [(1813, 4), 7012, 53]-NRT-code) | [i] | ||
| 5 | Linear OOA(3240, 1813, F3, 5, 52) (dual of [(1813, 5), 8825, 53]-NRT-code) | [i] | ||
| 6 | Digital (188, 240, 1813)-net over F3 | [i] | ||
| 7 | Linear OA(3247, 2217, F3, 52) (dual of [2217, 1970, 53]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(3248, 2227, F3, 52) (dual of [2227, 1979, 53]-code) | [i] | ||
| 9 | Linear OA(3249, 2241, F3, 52) (dual of [2241, 1992, 53]-code) | [i] | ||
| 10 | Linear OA(3250, 2260, F3, 52) (dual of [2260, 2010, 53]-code) | [i] | ||
| 11 | Linear OOA(3240, 1097, F3, 2, 52) (dual of [(1097, 2), 1954, 53]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3240, 731, F3, 3, 52) (dual of [(731, 3), 1953, 53]-NRT-code) | [i] | ||
| 13 | Linear OOA(3240, 548, F3, 4, 52) (dual of [(548, 4), 1952, 53]-NRT-code) | [i] | ||
| 14 | Linear OOA(3240, 439, F3, 5, 52) (dual of [(439, 5), 1955, 53]-NRT-code) | [i] | ||