Information on Result #679200
Linear OA(4140, 16432, F4, 25) (dual of [16432, 16292, 26]-code), using construction X applied to Ce(24) ⊂ Ce(17) based on
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(413, 48, F4, 6) (dual of [48, 35, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-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(4141, 16433, F4, 25) (dual of [16433, 16292, 26]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4142, 16434, F4, 25) (dual of [16434, 16292, 26]-code) | [i] | ||
| 3 | Linear OA(4139, 16431, F4, 24) (dual of [16431, 16292, 25]-code) | [i] | Truncation | |
| 4 | Linear OOA(4140, 13655, F4, 2, 25) (dual of [(13655, 2), 27170, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(4140, 13655, F4, 3, 25) (dual of [(13655, 3), 40825, 26]-NRT-code) | [i] | ||
| 6 | Digital (115, 140, 13655)-net over F4 | [i] | ||
| 7 | Linear OA(4142, 16435, F4, 25) (dual of [16435, 16293, 26]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(4140, 8216, F4, 2, 25) (dual of [(8216, 2), 16292, 26]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(4140, 5477, F4, 3, 25) (dual of [(5477, 3), 16291, 26]-NRT-code) | [i] | ||
| 10 | Linear OOA(4140, 1369, F4, 25, 25) (dual of [(1369, 25), 34085, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |