Information on Result #1418706
Linear OOA(3240, 2181, F3, 2, 50) (dual of [(2181, 2), 4122, 51]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3240, 2181, F3, 50) (dual of [2181, 1941, 51]-code), using
- discarding factors / shortening the dual code based on linear OA(3240, 2217, F3, 50) (dual of [2217, 1977, 51]-code), using
- construction XX applied to Ce(49) ⊂ Ce(45) ⊂ Ce(43) [i] based on
- 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(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3204, 2187, F3, 44) (dual of [2187, 1983, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(49) ⊂ Ce(45) ⊂ Ce(43) [i] based on
Mode: 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(3240, 1090, F3, 3, 50) (dual of [(1090, 3), 3030, 51]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3240, 1090, F3, 4, 50) (dual of [(1090, 4), 4120, 51]-NRT-code) | [i] | ||