Information on Result #2244580
Linear OA(4238, 16412, F4, 44) (dual of [16412, 16174, 45]-code), using 1 times truncation based on linear OA(4239, 16413, F4, 45) (dual of [16413, 16174, 46]-code), using
- construction XX applied to Ce(44) ⊂ Ce(40) ⊂ Ce(38) [i] based on
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4204, 16384, F4, 39) (dual of [16384, 16180, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4238, 13707, F4, 2, 44) (dual of [(13707, 2), 27176, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4238, 13707, F4, 3, 44) (dual of [(13707, 3), 40883, 45]-NRT-code) | [i] | ||
| 3 | Digital (194, 238, 13707)-net over F4 | [i] | ||
| 4 | Linear OOA(4238, 8206, F4, 2, 44) (dual of [(8206, 2), 16174, 45]-NRT-code) | [i] | OOA Folding | |