Information on Result #679224
Linear OA(4119, 16439, F4, 20) (dual of [16439, 16320, 21]-code), using construction X applied to Ce(20) ⊂ Ce(12) based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(413, 55, F4, 6) (dual of [55, 42, 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 OOA(4119, 16439, F4, 2, 20) (dual of [(16439, 2), 32759, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4119, 16439, F4, 3, 20) (dual of [(16439, 3), 49198, 21]-NRT-code) | [i] | ||
| 3 | Digital (99, 119, 16439)-net over F4 | [i] | ||
| 4 | Linear OOA(4119, 8219, F4, 2, 20) (dual of [(8219, 2), 16319, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4119, 5479, F4, 3, 20) (dual of [(5479, 3), 16318, 21]-NRT-code) | [i] | ||