Information on Result #683977
Linear OA(5141, 162, F5, 83) (dual of [162, 21, 84]-code), using construction XX applied to C1 = C([0,77]), C2 = C([1,80]), C3 = C1 + C2 = C([1,77]), and C∩ = C1 ∩ C2 = C([0,80]) based on
- linear OA(5136, 156, F5, 80) (dual of [156, 20, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 156 | 54−1, defining interval I = [0,77], and minimum distance d ≥ |{−2,−1,…,77}|+1 = 81 (BCH-bound) [i]
- linear OA(5136, 156, F5, 80) (dual of [156, 20, 81]-code), using the narrow-sense BCH-code C(I) with length 156 | 54−1, defining interval I = [1,80], and designed minimum distance d ≥ |I|+1 = 81 [i]
- linear OA(5137, 156, F5, 83) (dual of [156, 19, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 156 | 54−1, defining interval I = [0,80], and minimum distance d ≥ |{−2,−1,…,80}|+1 = 84 (BCH-bound) [i]
- linear OA(5135, 156, F5, 77) (dual of [156, 21, 78]-code), using the narrow-sense BCH-code C(I) with length 156 | 54−1, defining interval I = [1,77], and designed minimum distance d ≥ |I|+1 = 78 [i]
- linear OA(52, 3, F5, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,5)), using
- dual of repetition code with length 3 [i]
- linear OA(52, 3, F5, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,5)) (see above)
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(5140, 161, F5, 82) (dual of [161, 21, 83]-code) | [i] | Truncation | |
| 2 | Linear OOA(5141, 81, F5, 2, 83) (dual of [(81, 2), 21, 84]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(5141, 54, F5, 3, 83) (dual of [(54, 3), 21, 84]-NRT-code) | [i] | ||