Information on Result #685787
Linear OA(7110, 119, F7, 80) (dual of [119, 9, 81]-code), using construction XX applied to C1 = C([0,75]), C2 = C([1,78]), C3 = C1 + C2 = C([1,75]), and C∩ = C1 ∩ C2 = C([0,78]) based on
- linear OA(7106, 114, F7, 78) (dual of [114, 8, 79]-code), using the expurgated narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [0,75], and minimum distance d ≥ |{−2,−1,…,75}|+1 = 79 (BCH-bound) [i]
- linear OA(7106, 114, F7, 78) (dual of [114, 8, 79]-code), using the narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [1,78], and designed minimum distance d ≥ |I|+1 = 79 [i]
- linear OA(7107, 114, F7, 81) (dual of [114, 7, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [0,78], and minimum distance d ≥ |{−2,−1,…,78}|+1 = 82 (BCH-bound) [i]
- linear OA(7105, 114, F7, 75) (dual of [114, 9, 76]-code), using the narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [1,75], and designed minimum distance d ≥ |I|+1 = 76 [i]
- linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- linear OA(72, 3, F7, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,7)), using
- dual of repetition code with length 3 [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 OA(7107, 116, F7, 77) (dual of [116, 9, 78]-code) | [i] | Truncation | |
| 2 | Linear OA(7106, 115, F7, 76) (dual of [115, 9, 77]-code) | [i] | ||