Information on Result #679944
Linear OA(4165, 4105, F4, 37) (dual of [4105, 3940, 38]-code), using construction XX applied to Ce(36) ⊂ Ce(34) ⊂ Ce(33) based on
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 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(4151, 4096, F4, 34) (dual of [4096, 3945, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(41, 8, F4, 1) (dual of [8, 7, 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(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(4165, 3043, F4, 2, 37) (dual of [(3043, 2), 5921, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4165, 3043, F4, 3, 37) (dual of [(3043, 3), 8964, 38]-NRT-code) | [i] | ||
| 3 | Digital (128, 165, 3043)-net over F4 | [i] | ||
| 4 | Linear OOA(4165, 2052, F4, 2, 37) (dual of [(2052, 2), 3939, 38]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4165, 1368, F4, 3, 37) (dual of [(1368, 3), 3939, 38]-NRT-code) | [i] | ||