Information on Result #682126
Linear OA(5146, 1953135, F5, 21) (dual of [1953135, 1952989, 22]-code), using construction X applied to Ce(20) ⊂ Ce(18) based on
- linear OA(5145, 1953125, F5, 21) (dual of [1953125, 1952980, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(5136, 1953125, F5, 19) (dual of [1953125, 1952989, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(51, 10, F5, 1) (dual of [10, 9, 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
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(5147, 1953136, F5, 21) (dual of [1953136, 1952989, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5145, 1953134, F5, 20) (dual of [1953134, 1952989, 21]-code) | [i] | Truncation | |
| 3 | Linear OOA(5146, 976567, F5, 2, 21) (dual of [(976567, 2), 1952988, 22]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(5146, 651045, F5, 3, 21) (dual of [(651045, 3), 1952989, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(5146, 195313, F5, 21, 21) (dual of [(195313, 21), 4101427, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |