Information on Result #683203
Linear OA(574, 3139, F5, 18) (dual of [3139, 3065, 19]-code), using construction XX applied to Ce(17) ⊂ Ce(15) ⊂ Ce(13) based on
- linear OA(571, 3125, F5, 18) (dual of [3125, 3054, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(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(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(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(574, 2617, F5, 2, 18) (dual of [(2617, 2), 5160, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(574, 2617, F5, 3, 18) (dual of [(2617, 3), 7777, 19]-NRT-code) | [i] | ||
| 3 | Digital (56, 74, 2617)-net over F5 | [i] | ||
| 4 | Linear OOA(574, 1046, F5, 3, 18) (dual of [(1046, 3), 3064, 19]-NRT-code) | [i] | OOA Folding | |