Information on Result #678782
Linear OA(4134, 65597, F4, 20) (dual of [65597, 65463, 21]-code), using construction X applied to Ce(20) ⊂ Ce(12) based on
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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 OOA(4134, 65597, F4, 2, 20) (dual of [(65597, 2), 131060, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4134, 65597, F4, 3, 20) (dual of [(65597, 3), 196657, 21]-NRT-code) | [i] | ||
| 3 | Digital (114, 134, 65597)-net over F4 | [i] | ||
| 4 | Linear OOA(4134, 32798, F4, 2, 20) (dual of [(32798, 2), 65462, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4134, 21865, F4, 3, 20) (dual of [(21865, 3), 65461, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(4134, 6559, F4, 20, 20) (dual of [(6559, 20), 131046, 21]-NRT-code) | [i] | OA Folding and Stacking | |