Information on Result #679981
Linear OA(4111, 4111, F4, 24) (dual of [4111, 4000, 25]-code), using construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(20) based on
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(497, 4096, F4, 22) (dual of [4096, 3999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(41, 14, F4, 1) (dual of [14, 13, 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(4111, 3073, F4, 2, 24) (dual of [(3073, 2), 6035, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4111, 3073, F4, 3, 24) (dual of [(3073, 3), 9108, 25]-NRT-code) | [i] | ||
| 3 | Digital (87, 111, 3073)-net over F4 | [i] | ||
| 4 | Linear OOA(4111, 2055, F4, 2, 24) (dual of [(2055, 2), 3999, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4111, 1370, F4, 3, 24) (dual of [(1370, 3), 3999, 25]-NRT-code) | [i] | ||