Information on Result #683039
Linear OA(559, 3143, F5, 14) (dual of [3143, 3084, 15]-code), using construction X applied to Ce(13) ⊂ Ce(10) based on
- linear OA(556, 3125, F5, 14) (dual of [3125, 3069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(541, 3125, F5, 11) (dual of [3125, 3084, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(53, 18, F5, 2) (dual of [18, 15, 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(560, 3144, F5, 14) (dual of [3144, 3084, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(560, 3145, F5, 14) (dual of [3145, 3085, 15]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OA(561, 3147, F5, 14) (dual of [3147, 3086, 15]-code) | [i] | ||
| 4 | Linear OOA(559, 1571, F5, 2, 14) (dual of [(1571, 2), 3083, 15]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(559, 1047, F5, 3, 14) (dual of [(1047, 3), 3082, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(559, 449, F5, 14, 14) (dual of [(449, 14), 6227, 15]-NRT-code) | [i] | OA Folding and Stacking | |