Information on Result #682704
Linear OA(546, 15646, F5, 9) (dual of [15646, 15600, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 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(53, 21, F5, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-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(547, 15647, F5, 9) (dual of [15647, 15600, 10]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(546, 15646, F5, 2, 9) (dual of [(15646, 2), 31246, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(546, 15646, F5, 3, 9) (dual of [(15646, 3), 46892, 10]-NRT-code) | [i] | ||
| 4 | Digital (37, 46, 15646)-net over F5 | [i] | ||
| 5 | Linear OA(547, 15648, F5, 9) (dual of [15648, 15601, 10]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(548, 15650, F5, 9) (dual of [15650, 15602, 10]-code) | [i] | ||
| 7 | Linear OOA(546, 7823, F5, 2, 9) (dual of [(7823, 2), 15600, 10]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(546, 5215, F5, 3, 9) (dual of [(5215, 3), 15599, 10]-NRT-code) | [i] | ||
| 9 | Linear OOA(546, 3911, F5, 9, 9) (dual of [(3911, 9), 35153, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |