Information on Result #682172
Linear OA(529, 1953145, F5, 4) (dual of [1953145, 1953116, 5]-code), using construction X4 applied to Ce(3) ⊂ Ce(1) based on
- linear OA(528, 1953125, F5, 4) (dual of [1953125, 1953097, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(510, 1953125, F5, 2) (dual of [1953125, 1953115, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
- dual of repetition code with length 20 [i]
- linear OA(51, 20, F5, 1) (dual of [20, 19, 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(530, 1953146, F5, 4) (dual of [1953146, 1953116, 5]-code) | [i] | Code Embedding in Larger Space | |