Information on Result #683199
Linear OA(578, 3138, F5, 19) (dual of [3138, 3060, 20]-code), using construction XX applied to Ce(18) ⊂ Ce(16) ⊂ Ce(15) based on
- linear OA(576, 3125, F5, 19) (dual of [3125, 3049, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(566, 3125, F5, 17) (dual of [3125, 3059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(51, 12, F5, 1) (dual of [12, 11, 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(578, 2618, F5, 2, 19) (dual of [(2618, 2), 5158, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(578, 2618, F5, 3, 19) (dual of [(2618, 3), 7776, 20]-NRT-code) | [i] | ||
| 3 | Digital (59, 78, 2618)-net over F5 | [i] | ||
| 4 | Linear OOA(578, 1569, F5, 2, 19) (dual of [(1569, 2), 3060, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(578, 1046, F5, 3, 19) (dual of [(1046, 3), 3060, 20]-NRT-code) | [i] | ||