Information on Result #682762
Linear OA(5127, 15673, F5, 24) (dual of [15673, 15546, 25]-code), using construction X applied to Ce(23) ⊂ Ce(16) based on
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(512, 48, F5, 6) (dual of [48, 36, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
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 OA(5128, 15674, F5, 24) (dual of [15674, 15546, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5127, 7836, F5, 2, 24) (dual of [(7836, 2), 15545, 25]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(5127, 5224, F5, 3, 24) (dual of [(5224, 3), 15545, 25]-NRT-code) | [i] | ||
| 4 | Linear OOA(5127, 1306, F5, 24, 24) (dual of [(1306, 24), 31217, 25]-NRT-code) | [i] | OA Folding and Stacking | |