Information on Result #710367
Linear OA(5129, 156, F5, 74) (dual of [156, 27, 75]-code), using construction XX applied to C1 = C([114,61]), C2 = C([1,63]), C3 = C1 + C2 = C([1,61]), and C∩ = C1 ∩ C2 = C([114,63]) 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(5101, 124, F5, 63) (dual of [124, 23, 64]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(5114, 124, F5, 74) (dual of [124, 10, 75]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−10,−9,…,63}, and designed minimum distance d ≥ |I|+1 = 75 [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(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [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(5129, 156, F5, 73) (dual of [156, 27, 74]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5129, 156, F5, 72) (dual of [156, 27, 73]-code) | [i] | ||
| 3 | Linear OA(5130, 157, F5, 74) (dual of [157, 27, 75]-code) | [i] | Code Embedding in Larger Space | |
| 4 | Linear OA(5131, 158, F5, 74) (dual of [158, 27, 75]-code) | [i] | ||
| 5 | Linear OA(5132, 159, F5, 74) (dual of [159, 27, 75]-code) | [i] | ||
| 6 | Linear OA(5128, 155, F5, 73) (dual of [155, 27, 74]-code) | [i] | Truncation | |
| 7 | Linear OA(5127, 154, F5, 72) (dual of [154, 27, 73]-code) | [i] | ||
| 8 | Linear OA(5126, 153, F5, 71) (dual of [153, 27, 72]-code) | [i] | ||
| 9 | Linear OA(5125, 152, F5, 70) (dual of [152, 27, 71]-code) | [i] | ||
| 10 | Linear OA(5123, 150, F5, 68) (dual of [150, 27, 69]-code) | [i] | ||
| 11 | Linear OOA(5129, 78, F5, 2, 74) (dual of [(78, 2), 27, 75]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(5129, 52, F5, 3, 74) (dual of [(52, 3), 27, 75]-NRT-code) | [i] | ||