Information on Result #679957
Linear OA(4147, 4111, F4, 32) (dual of [4111, 3964, 33]-code), using construction XX applied to Ce(32) ⊂ Ce(29) ⊂ Ce(28) based on
- 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(4133, 4096, F4, 30) (dual of [4096, 3963, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(4147, 3394, F4, 2, 32) (dual of [(3394, 2), 6641, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4147, 3394, F4, 3, 32) (dual of [(3394, 3), 10035, 33]-NRT-code) | [i] | ||
| 3 | Digital (115, 147, 3394)-net over F4 | [i] | ||
| 4 | Linear OOA(4147, 2055, F4, 2, 32) (dual of [(2055, 2), 3963, 33]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4147, 1370, F4, 3, 32) (dual of [(1370, 3), 3963, 33]-NRT-code) | [i] | ||