Information on Result #682291
Linear OA(544, 390644, F5, 7) (dual of [390644, 390600, 8]-code), using construction X applied to Ce(6) ⊂ Ce(3) based on
- linear OA(541, 390625, F5, 7) (dual of [390625, 390584, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(525, 390625, F5, 4) (dual of [390625, 390600, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(53, 19, F5, 2) (dual of [19, 16, 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 OOA(544, 390644, F5, 2, 7) (dual of [(390644, 2), 781244, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(544, 390644, F5, 3, 7) (dual of [(390644, 3), 1171888, 8]-NRT-code) | [i] | ||
| 3 | Digital (37, 44, 390644)-net over F5 | [i] | ||
| 4 | Linear OOA(544, 195322, F5, 2, 7) (dual of [(195322, 2), 390600, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(544, 130214, F5, 3, 7) (dual of [(130214, 3), 390598, 8]-NRT-code) | [i] | ||