Information on Result #683043
Linear OA(539, 3143, F5, 9) (dual of [3143, 3104, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
- linear OA(536, 3125, F5, 9) (dual of [3125, 3089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(521, 3125, F5, 6) (dual of [3125, 3104, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(540, 3144, F5, 9) (dual of [3144, 3104, 10]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(540, 3145, F5, 9) (dual of [3145, 3105, 10]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(539, 1571, F5, 2, 9) (dual of [(1571, 2), 3103, 10]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(539, 1047, F5, 3, 9) (dual of [(1047, 3), 3102, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(539, 785, F5, 9, 9) (dual of [(785, 9), 7026, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |