Information on Result #679953
Linear OA(4153, 4105, F4, 34) (dual of [4105, 3952, 35]-code), using construction XX applied to Ce(33) ⊂ Ce(32) ⊂ Ce(30) based on
- 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(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(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(4153, 3062, F4, 2, 34) (dual of [(3062, 2), 5971, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4153, 3062, F4, 3, 34) (dual of [(3062, 3), 9033, 35]-NRT-code) | [i] | ||
| 3 | Digital (119, 153, 3062)-net over F4 | [i] | ||
| 4 | Linear OOA(4153, 1368, F4, 3, 34) (dual of [(1368, 3), 3951, 35]-NRT-code) | [i] | OOA Folding | |