Information on Result #676139
Linear OA(3243, 2207, F3, 51) (dual of [2207, 1964, 52]-code), using construction XX applied to Ce(51) ⊂ Ce(48) ⊂ Ce(46) 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(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(3218, 2187, F3, 47) (dual of [2187, 1969, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 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, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [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(3243, 2126, F3, 2, 51) (dual of [(2126, 2), 4009, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3243, 2126, F3, 3, 51) (dual of [(2126, 3), 6135, 52]-NRT-code) | [i] | ||
| 3 | Linear OOA(3243, 2126, F3, 4, 51) (dual of [(2126, 4), 8261, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(3243, 2126, F3, 5, 51) (dual of [(2126, 5), 10387, 52]-NRT-code) | [i] | ||
| 5 | Digital (192, 243, 2126)-net over F3 | [i] | ||