Information on Result #686378
Linear OA(8167, 2097179, F8, 27) (dual of [2097179, 2097012, 28]-code), using construction XX applied to Ce(26) ⊂ Ce(22) ⊂ Ce(21) based on
- linear OA(8162, 2097152, F8, 27) (dual of [2097152, 2096990, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(8167, 1442251, F8, 2, 27) (dual of [(1442251, 2), 2884335, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8167, 1442251, F8, 3, 27) (dual of [(1442251, 3), 4326586, 28]-NRT-code) | [i] | ||
| 3 | Digital (140, 167, 1442251)-net over F8 | [i] | ||
| 4 | Linear OOA(8167, 1048589, F8, 2, 27) (dual of [(1048589, 2), 2097011, 28]-NRT-code) | [i] | OOA Folding | |