Information on Result #682758
Linear OA(5145, 15673, F5, 28) (dual of [15673, 15528, 29]-code), using construction X applied to Ce(27) ⊂ Ce(20) based on
- linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(512, 48, F5, 6) (dual of [48, 36, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), 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(5146, 15674, F5, 28) (dual of [15674, 15528, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5147, 15675, F5, 28) (dual of [15675, 15528, 29]-code) | [i] | ||
| 3 | Linear OA(5148, 15676, F5, 28) (dual of [15676, 15528, 29]-code) | [i] | ||
| 4 | Linear OA(5149, 15677, F5, 28) (dual of [15677, 15528, 29]-code) | [i] | ||
| 5 | Linear OA(5150, 15678, F5, 28) (dual of [15678, 15528, 29]-code) | [i] | ||
| 6 | Linear OOA(5145, 15673, F5, 2, 28) (dual of [(15673, 2), 31201, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(5145, 15673, F5, 3, 28) (dual of [(15673, 3), 46874, 29]-NRT-code) | [i] | ||
| 8 | Digital (117, 145, 15673)-net over F5 | [i] | ||
| 9 | Linear OOA(5145, 7836, F5, 2, 28) (dual of [(7836, 2), 15527, 29]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(5145, 5224, F5, 3, 28) (dual of [(5224, 3), 15527, 29]-NRT-code) | [i] | ||