Information on Result #679809
Linear OA(4251, 4148, F4, 53) (dual of [4148, 3897, 54]-code), using construction X applied to Ce(52) ⊂ Ce(44) based on
- linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(416, 52, F4, 7) (dual of [52, 36, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), 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(4251, 4148, F4, 52) (dual of [4148, 3897, 53]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4252, 4149, F4, 53) (dual of [4149, 3897, 54]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4253, 4150, F4, 53) (dual of [4150, 3897, 54]-code) | [i] | ||
| 4 | Linear OA(4250, 4147, F4, 52) (dual of [4147, 3897, 53]-code) | [i] | Truncation | |
| 5 | Linear OOA(4251, 2074, F4, 2, 53) (dual of [(2074, 2), 3897, 54]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4251, 1382, F4, 3, 53) (dual of [(1382, 3), 3895, 54]-NRT-code) | [i] | ||