Information on Result #2272595
Linear OA(4183, 65598, F4, 28) (dual of [65598, 65415, 29]-code), using 1 times code embedding in larger space based on linear OA(4182, 65597, F4, 28) (dual of [65597, 65415, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- 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(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(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(4183, 57602, F4, 2, 28) (dual of [(57602, 2), 115021, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4183, 57602, F4, 3, 28) (dual of [(57602, 3), 172623, 29]-NRT-code) | [i] | ||
| 3 | Digital (155, 183, 57602)-net over F4 | [i] | ||
| 4 | Linear OOA(4183, 32799, F4, 2, 28) (dual of [(32799, 2), 65415, 29]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4183, 21866, F4, 3, 28) (dual of [(21866, 3), 65415, 29]-NRT-code) | [i] | ||