Information on Result #679828
Linear OA(4254, 4157, F4, 53) (dual of [4157, 3903, 54]-code), using construction X applied to Ce(52) ⊂ Ce(42) 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(4193, 4096, F4, 43) (dual of [4096, 3903, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(419, 61, F4, 9) (dual of [61, 42, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(419, 63, F4, 9) (dual of [63, 44, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(419, 63, F4, 9) (dual of [63, 44, 10]-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(4255, 4158, F4, 53) (dual of [4158, 3903, 54]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4256, 4159, F4, 53) (dual of [4159, 3903, 54]-code) | [i] | ||
| 3 | Linear OA(4253, 4156, F4, 52) (dual of [4156, 3903, 53]-code) | [i] | Truncation | |
| 4 | Linear OOA(4254, 2078, F4, 2, 53) (dual of [(2078, 2), 3902, 54]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4254, 1385, F4, 3, 53) (dual of [(1385, 3), 3901, 54]-NRT-code) | [i] | ||