Information on Result #682776
Linear OA(5147, 15634, F5, 31) (dual of [15634, 15487, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(28) ⊂ Ce(27) based on
- linear OA(5145, 15625, F5, 31) (dual of [15625, 15480, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(51, 8, F5, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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 OOA(5147, 9618, F5, 2, 31) (dual of [(9618, 2), 19089, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5147, 9618, F5, 3, 31) (dual of [(9618, 3), 28707, 32]-NRT-code) | [i] | ||
| 3 | Digital (116, 147, 9618)-net over F5 | [i] | ||
| 4 | Linear OOA(5147, 7817, F5, 2, 31) (dual of [(7817, 2), 15487, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5147, 5211, F5, 3, 31) (dual of [(5211, 3), 15486, 32]-NRT-code) | [i] | ||