Information on Result #682814
Linear OA(599, 15634, F5, 21) (dual of [15634, 15535, 22]-code), using construction XX applied to Ce(20) ⊂ Ce(18) ⊂ Ce(17) based on
- 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(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(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(599, 7974, F5, 2, 21) (dual of [(7974, 2), 15849, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(599, 7974, F5, 3, 21) (dual of [(7974, 3), 23823, 22]-NRT-code) | [i] | ||
| 3 | Digital (78, 99, 7974)-net over F5 | [i] | ||
| 4 | Linear OOA(599, 7817, F5, 2, 21) (dual of [(7817, 2), 15535, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(599, 5211, F5, 3, 21) (dual of [(5211, 3), 15534, 22]-NRT-code) | [i] | ||