Information on Result #683856
Linear OA(519, 632, F5, 6) (dual of [632, 613, 7]-code), using construction XX applied to Ce(5) ⊂ Ce(3) ⊂ Ce(2) based on
- linear OA(517, 625, F5, 6) (dual of [625, 608, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(513, 625, F5, 4) (dual of [625, 612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(59, 625, F5, 3) (dual of [625, 616, 4]-code or 625-cap in PG(8,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(51, 6, F5, 1) (dual of [6, 5, 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(519, 316, F5, 2, 6) (dual of [(316, 2), 613, 7]-NRT-code) | [i] | OOA Folding | |