Information on Result #679932
Linear OA(4183, 4105, F4, 41) (dual of [4105, 3922, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(38) ⊂ Ce(37) based on
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4175, 4096, F4, 39) (dual of [4096, 3921, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(4183, 3280, F4, 2, 41) (dual of [(3280, 2), 6377, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4183, 3280, F4, 3, 41) (dual of [(3280, 3), 9657, 42]-NRT-code) | [i] | ||
| 3 | Digital (142, 183, 3280)-net over F4 | [i] | ||
| 4 | Linear OOA(4183, 2052, F4, 2, 41) (dual of [(2052, 2), 3921, 42]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4183, 1368, F4, 3, 41) (dual of [(1368, 3), 3921, 42]-NRT-code) | [i] | ||