Information on Result #678478
Linear OA(4119, 262199, F4, 16) (dual of [262199, 262080, 17]-code), using construction X applied to Ce(16) ⊂ Ce(9) based on
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(464, 262144, F4, 10) (dual of [262144, 262080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(410, 55, F4, 5) (dual of [55, 45, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-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, 239234, F4, 2, 16) (dual of [(239234, 2), 478349, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4119, 239234, F4, 3, 16) (dual of [(239234, 3), 717583, 17]-NRT-code) | [i] | ||
| 3 | Digital (103, 119, 239234)-net over F4 | [i] | ||
| 4 | Linear OOA(4119, 131099, F4, 2, 16) (dual of [(131099, 2), 262079, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4119, 87399, F4, 3, 16) (dual of [(87399, 3), 262078, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(4119, 32774, F4, 16, 16) (dual of [(32774, 16), 524265, 17]-NRT-code) | [i] | OA Folding and Stacking | |