Information on Result #678774
Linear OA(4230, 65597, F4, 36) (dual of [65597, 65367, 37]-code), using construction X applied to Ce(36) ⊂ Ce(28) based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-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(4231, 65598, F4, 36) (dual of [65598, 65367, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4234, 65601, F4, 36) (dual of [65601, 65367, 37]-code) | [i] | ||
| 3 | Linear OA(4235, 65602, F4, 36) (dual of [65602, 65367, 37]-code) | [i] | ||
| 4 | Linear OOA(4230, 51189, F4, 2, 36) (dual of [(51189, 2), 102148, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(4230, 51189, F4, 3, 36) (dual of [(51189, 3), 153337, 37]-NRT-code) | [i] | ||
| 6 | Digital (194, 230, 51189)-net over F4 | [i] | ||
| 7 | Linear OA(4232, 65600, F4, 36) (dual of [65600, 65368, 37]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(4233, 65602, F4, 36) (dual of [65602, 65369, 37]-code) | [i] | ||
| 9 | Linear OA(4234, 65604, F4, 36) (dual of [65604, 65370, 37]-code) | [i] | ||
| 10 | Linear OA(4235, 65606, F4, 36) (dual of [65606, 65371, 37]-code) | [i] | ||
| 11 | Linear OA(4236, 65608, F4, 36) (dual of [65608, 65372, 37]-code) | [i] | ||
| 12 | Linear OA(4237, 65610, F4, 36) (dual of [65610, 65373, 37]-code) | [i] | ||
| 13 | Linear OOA(4230, 32798, F4, 2, 36) (dual of [(32798, 2), 65366, 37]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(4230, 21865, F4, 3, 36) (dual of [(21865, 3), 65365, 37]-NRT-code) | [i] | ||
| 15 | Linear OOA(4230, 3644, F4, 36, 36) (dual of [(3644, 36), 130954, 37]-NRT-code) | [i] | OA Folding and Stacking | |