Information on Result #710417
Linear OA(5135, 162, F5, 76) (dual of [162, 27, 77]-code), using construction XX applied to C1 = C([114,61]), C2 = C([1,67]), C3 = C1 + C2 = C([1,61]), and C∩ = C1 ∩ C2 = C([114,67]) based on
- linear OA(5110, 124, F5, 72) (dual of [124, 14, 73]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−10,−9,…,61}, and designed minimum distance d ≥ |I|+1 = 73 [i]
- linear OA(5104, 124, F5, 67) (dual of [124, 20, 68]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,67], and designed minimum distance d ≥ |I|+1 = 68 [i]
- linear OA(5117, 124, F5, 78) (dual of [124, 7, 79]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−10,−9,…,67}, and designed minimum distance d ≥ |I|+1 = 79 [i]
- linear OA(597, 124, F5, 61) (dual of [124, 27, 62]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,61], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(514, 27, F5, 10) (dual of [27, 13, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(514, 29, F5, 10) (dual of [29, 15, 11]-code), using
- 1 times truncation [i] based on linear OA(515, 30, F5, 11) (dual of [30, 15, 12]-code), using
- extended quadratic residue code Qe(30,5) [i]
- 1 times truncation [i] based on linear OA(515, 30, F5, 11) (dual of [30, 15, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(514, 29, F5, 10) (dual of [29, 15, 11]-code), using
- linear OA(54, 11, F5, 3) (dual of [11, 7, 4]-code or 11-cap in PG(3,5)), using
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(5135, 162, F5, 75) (dual of [162, 27, 76]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5135, 162, F5, 74) (dual of [162, 27, 75]-code) | [i] | ||
| 3 | Linear OA(5134, 161, F5, 75) (dual of [161, 27, 76]-code) | [i] | Truncation | |
| 4 | Linear OA(5133, 160, F5, 74) (dual of [160, 27, 75]-code) | [i] | ||
| 5 | Linear OA(5132, 159, F5, 73) (dual of [159, 27, 74]-code) | [i] | ||
| 6 | Linear OA(5131, 158, F5, 72) (dual of [158, 27, 73]-code) | [i] | ||
| 7 | Linear OOA(5135, 81, F5, 2, 76) (dual of [(81, 2), 27, 77]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(5135, 54, F5, 3, 76) (dual of [(54, 3), 27, 77]-NRT-code) | [i] | ||