Information on Result #686593
Linear OA(8168, 262174, F8, 31) (dual of [262174, 262006, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(26) ⊂ Ce(25) based on
- linear OA(8163, 262144, F8, 31) (dual of [262144, 261981, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8139, 262144, F8, 27) (dual of [262144, 262005, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(84, 29, F8, 3) (dual of [29, 25, 4]-code or 29-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(8168, 262174, F8, 2, 31) (dual of [(262174, 2), 524180, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8168, 262174, F8, 3, 31) (dual of [(262174, 3), 786354, 32]-NRT-code) | [i] | ||
| 3 | Digital (137, 168, 262174)-net over F8 | [i] | ||
| 4 | Linear OOA(8168, 131087, F8, 2, 31) (dual of [(131087, 2), 262006, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8168, 87391, F8, 3, 31) (dual of [(87391, 3), 262005, 32]-NRT-code) | [i] | ||