Information on Result #682821
Linear OA(593, 15640, F5, 19) (dual of [15640, 15547, 20]-code), using construction XX applied to Ce(18) ⊂ Ce(16) ⊂ Ce(15) based on
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(51, 14, F5, 1) (dual of [14, 13, 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(593, 10866, F5, 2, 19) (dual of [(10866, 2), 21639, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(593, 10866, F5, 3, 19) (dual of [(10866, 3), 32505, 20]-NRT-code) | [i] | ||
| 3 | Digital (74, 93, 10866)-net over F5 | [i] | ||
| 4 | Linear OOA(593, 7820, F5, 2, 19) (dual of [(7820, 2), 15547, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(593, 5213, F5, 3, 19) (dual of [(5213, 3), 15546, 20]-NRT-code) | [i] | ||