Information on Result #686992
Linear OA(8171, 32794, F8, 38) (dual of [32794, 32623, 39]-code), using construction XX applied to Ce(37) ⊂ Ce(33) ⊂ Ce(32) based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(84, 25, F8, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,8)), using
- linear OA(80, 1, F8, 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(8171, 32794, F8, 2, 38) (dual of [(32794, 2), 65417, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8171, 32794, F8, 3, 38) (dual of [(32794, 3), 98211, 39]-NRT-code) | [i] | ||
| 3 | Digital (133, 171, 32794)-net over F8 | [i] | ||
| 4 | Linear OOA(8171, 16397, F8, 2, 38) (dual of [(16397, 2), 32623, 39]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8171, 10931, F8, 3, 38) (dual of [(10931, 3), 32622, 39]-NRT-code) | [i] | ||
| 6 | Linear OOA(8171, 1726, F8, 38, 38) (dual of [(1726, 38), 65417, 39]-NRT-code) | [i] | OA Folding and Stacking | |