Information on Result #682656
Linear OA(526, 15633, F5, 6) (dual of [15633, 15607, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(3) based on
- linear OA(525, 15625, F5, 6) (dual of [15625, 15600, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(519, 15625, F5, 4) (dual of [15625, 15606, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(57, 8, F5, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,5)), using
- dual of repetition code with length 8 [i]
- linear OA(51, 8, F5, 1) (dual of [8, 7, 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(527, 15634, F5, 6) (dual of [15634, 15607, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(525, 15632, F5, 5) (dual of [15632, 15607, 6]-code) | [i] | Truncation | |
| 3 | Linear OA(527, 15635, F5, 6) (dual of [15635, 15608, 7]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(526, 5211, F5, 3, 6) (dual of [(5211, 3), 15607, 7]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(526, 5211, F5, 6, 6) (dual of [(5211, 6), 31240, 7]-NRT-code) | [i] | OA Folding and Stacking | |