Information on Result #686389
Linear OA(8111, 2097179, F8, 18) (dual of [2097179, 2097068, 19]-code), using construction XX applied to Ce(17) ⊂ Ce(13) ⊂ Ce(12) based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(84, 26, F8, 3) (dual of [26, 22, 4]-code or 26-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(8111, 1571020, F8, 2, 18) (dual of [(1571020, 2), 3141929, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8111, 1571020, F8, 3, 18) (dual of [(1571020, 3), 4712949, 19]-NRT-code) | [i] | ||
| 3 | Digital (93, 111, 1571020)-net over F8 | [i] | ||
| 4 | Linear OOA(8111, 1048589, F8, 2, 18) (dual of [(1048589, 2), 2097067, 19]-NRT-code) | [i] | OOA Folding | |