Information on Result #679837
Linear OA(4200, 4157, F4, 41) (dual of [4157, 3957, 42]-code), using construction X applied to Ce(40) ⊂ Ce(30) based on
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4139, 4096, F4, 31) (dual of [4096, 3957, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(4201, 4158, F4, 41) (dual of [4158, 3957, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4202, 4159, F4, 41) (dual of [4159, 3957, 42]-code) | [i] | ||
| 3 | Linear OA(4199, 4156, F4, 40) (dual of [4156, 3957, 41]-code) | [i] | Truncation | |
| 4 | Linear OOA(4200, 2078, F4, 2, 41) (dual of [(2078, 2), 3956, 42]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4200, 1385, F4, 3, 41) (dual of [(1385, 3), 3955, 42]-NRT-code) | [i] | ||