Information on Result #682831
Linear OA(581, 15634, F5, 17) (dual of [15634, 15553, 18]-code), using construction XX applied to Ce(16) ⊂ Ce(15) ⊂ Ce(13) based on
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(50, 7, F5, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(581, 8571, F5, 2, 17) (dual of [(8571, 2), 17061, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(581, 8571, F5, 3, 17) (dual of [(8571, 3), 25632, 18]-NRT-code) | [i] | ||
| 3 | Digital (64, 81, 8571)-net over F5 | [i] | ||
| 4 | Linear OOA(581, 7817, F5, 2, 17) (dual of [(7817, 2), 15553, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(581, 5211, F5, 3, 17) (dual of [(5211, 3), 15552, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(581, 1954, F5, 17, 17) (dual of [(1954, 17), 33137, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |