Information on Result #676136
Linear OA(3248, 2197, F3, 53) (dual of [2197, 1949, 54]-code), using construction XX applied to Ce(52) ⊂ Ce(51) ⊂ Ce(49) based on
- linear OA(3246, 2187, F3, 53) (dual of [2187, 1941, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- 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(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(3248, 1983, F3, 2, 53) (dual of [(1983, 2), 3718, 54]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3248, 1983, F3, 3, 53) (dual of [(1983, 3), 5701, 54]-NRT-code) | [i] | ||
| 3 | Linear OOA(3248, 1983, F3, 4, 53) (dual of [(1983, 4), 7684, 54]-NRT-code) | [i] | ||
| 4 | Linear OOA(3248, 1983, F3, 5, 53) (dual of [(1983, 5), 9667, 54]-NRT-code) | [i] | ||
| 5 | Digital (195, 248, 1983)-net over F3 | [i] | ||
| 6 | Linear OOA(3248, 732, F3, 3, 53) (dual of [(732, 3), 1948, 54]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3248, 549, F3, 4, 53) (dual of [(549, 4), 1948, 54]-NRT-code) | [i] | ||