Information on Result #683153
Linear OA(5123, 3133, F5, 31) (dual of [3133, 3010, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(28) ⊂ Ce(27) based on
- linear OA(5121, 3125, F5, 31) (dual of [3125, 3004, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(5116, 3125, F5, 29) (dual of [3125, 3009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(5111, 3125, F5, 28) (dual of [3125, 3014, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(5123, 2524, F5, 2, 31) (dual of [(2524, 2), 4925, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5123, 2524, F5, 3, 31) (dual of [(2524, 3), 7449, 32]-NRT-code) | [i] | ||
| 3 | Digital (92, 123, 2524)-net over F5 | [i] | ||
| 4 | Linear OOA(5123, 1566, F5, 2, 31) (dual of [(1566, 2), 3009, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5123, 1044, F5, 3, 31) (dual of [(1044, 3), 3009, 32]-NRT-code) | [i] | ||