Information on Result #683173
Linear OA(5103, 3133, F5, 26) (dual of [3133, 3030, 27]-code), using construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(22) based on
- linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(596, 3125, F5, 24) (dual of [3125, 3029, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(591, 3125, F5, 23) (dual of [3125, 3034, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(5103, 2274, F5, 2, 26) (dual of [(2274, 2), 4445, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5103, 2274, F5, 3, 26) (dual of [(2274, 3), 6719, 27]-NRT-code) | [i] | ||
| 3 | Digital (77, 103, 2274)-net over F5 | [i] | ||
| 4 | Linear OOA(5103, 1566, F5, 2, 26) (dual of [(1566, 2), 3029, 27]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5103, 1044, F5, 3, 26) (dual of [(1044, 3), 3029, 27]-NRT-code) | [i] | ||