Information on Result #679807
Linear OA(495, 4136, F4, 19) (dual of [4136, 4041, 20]-code), using construction X applied to Ce(18) ⊂ Ce(12) based on
- linear OA(485, 4096, F4, 19) (dual of [4096, 4011, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(455, 4096, F4, 13) (dual of [4096, 4041, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(410, 40, F4, 5) (dual of [40, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-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(496, 4137, F4, 19) (dual of [4137, 4041, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(497, 4138, F4, 19) (dual of [4138, 4041, 20]-code) | [i] | ||
| 3 | Linear OA(496, 4138, F4, 19) (dual of [4138, 4042, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(495, 2068, F4, 2, 19) (dual of [(2068, 2), 4041, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(495, 1378, F4, 3, 19) (dual of [(1378, 3), 4039, 20]-NRT-code) | [i] | ||