Information on Result #1301651
Linear OA(599, 1953170, F5, 13) (dual of [1953170, 1953071, 14]-code), using construction X with Varšamov bound based on
- linear OA(598, 1953168, F5, 13) (dual of [1953168, 1953070, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(591, 1953125, F5, 13) (dual of [1953125, 1953034, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(555, 1953125, F5, 8) (dual of [1953125, 1953070, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(57, 43, F5, 4) (dual of [43, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(598, 1953169, F5, 12) (dual of [1953169, 1953071, 13]-code), using Gilbert–Varšamov bound and bm = 598 > Vbs−1(k−1) = 165 816663 570414 808036 081693 373320 996736 819120 813401 943573 507869 931969 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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
Mode: 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, 1953170, F5, 2, 13) (dual of [(1953170, 2), 3906241, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(599, 1953170, F5, 3, 13) (dual of [(1953170, 3), 5859411, 14]-NRT-code) | [i] | ||
| 3 | Digital (86, 99, 1953170)-net over F5 | [i] | ||
| 4 | Linear OOA(599, 976585, F5, 2, 13) (dual of [(976585, 2), 1953071, 14]-NRT-code) | [i] | OOA Folding | |