Information on Result #683211
Linear OA(563, 3133, F5, 16) (dual of [3133, 3070, 17]-code), using construction XX applied to Ce(15) ⊂ Ce(13) ⊂ Ce(12) based on
- linear OA(561, 3125, F5, 16) (dual of [3125, 3064, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(556, 3125, F5, 14) (dual of [3125, 3069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(551, 3125, F5, 13) (dual of [3125, 3074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(51, 7, F5, 1) (dual of [7, 6, 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(563, 1874, F5, 2, 16) (dual of [(1874, 2), 3685, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(563, 1874, F5, 3, 16) (dual of [(1874, 3), 5559, 17]-NRT-code) | [i] | ||
| 3 | Digital (47, 63, 1874)-net over F5 | [i] | ||
| 4 | Linear OOA(563, 1566, F5, 2, 16) (dual of [(1566, 2), 3069, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(563, 1044, F5, 3, 16) (dual of [(1044, 3), 3069, 17]-NRT-code) | [i] | ||