Information on Result #683161
Linear OA(5118, 3138, F5, 29) (dual of [3138, 3020, 30]-code), using construction XX applied to Ce(28) ⊂ Ce(26) ⊂ Ce(25) based on
- 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(5106, 3125, F5, 27) (dual of [3125, 3019, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(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(5118, 2900, F5, 2, 29) (dual of [(2900, 2), 5682, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5118, 2900, F5, 3, 29) (dual of [(2900, 3), 8582, 30]-NRT-code) | [i] | ||
| 3 | Digital (89, 118, 2900)-net over F5 | [i] | ||
| 4 | Linear OOA(5118, 1569, F5, 2, 29) (dual of [(1569, 2), 3020, 30]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5118, 1046, F5, 3, 29) (dual of [(1046, 3), 3020, 30]-NRT-code) | [i] | ||