Information on Result #679950
Linear OA(4161, 4114, F4, 35) (dual of [4114, 3953, 36]-code), using construction XX applied to Ce(34) ⊂ Ce(32) ⊂ Ce(30) based on
- linear OA(4157, 4096, F4, 35) (dual of [4096, 3939, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4145, 4096, F4, 33) (dual of [4096, 3951, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(41, 15, F4, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-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(4161, 3616, F4, 2, 35) (dual of [(3616, 2), 7071, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4161, 3616, F4, 3, 35) (dual of [(3616, 3), 10687, 36]-NRT-code) | [i] | ||
| 3 | Digital (126, 161, 3616)-net over F4 | [i] | ||
| 4 | Linear OOA(4161, 2057, F4, 2, 35) (dual of [(2057, 2), 3953, 36]-NRT-code) | [i] | OOA Folding | |