Information on Result #683136
Linear OA(5148, 3133, F5, 37) (dual of [3133, 2985, 38]-code), using construction XX applied to Ce(36) ⊂ Ce(35) ⊂ Ce(33) based on
- linear OA(5146, 3125, F5, 37) (dual of [3125, 2979, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(5136, 3125, F5, 34) (dual of [3125, 2989, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(51, 2, F5, 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(5148, 2974, F5, 2, 37) (dual of [(2974, 2), 5800, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5148, 2974, F5, 3, 37) (dual of [(2974, 3), 8774, 38]-NRT-code) | [i] | ||
| 3 | Digital (111, 148, 2974)-net over F5 | [i] | ||
| 4 | Linear OOA(5148, 1044, F5, 3, 37) (dual of [(1044, 3), 2984, 38]-NRT-code) | [i] | OOA Folding | |