Information on Result #679206
Linear OA(4109, 16429, F4, 19) (dual of [16429, 16320, 20]-code), using construction X applied to Ce(18) ⊂ Ce(12) based on
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(410, 45, F4, 5) (dual of [45, 35, 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 OA(4110, 16430, F4, 19) (dual of [16430, 16320, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4111, 16431, F4, 19) (dual of [16431, 16320, 20]-code) | [i] | ||
| 3 | Linear OA(4112, 16432, F4, 19) (dual of [16432, 16320, 20]-code) | [i] | ||
| 4 | Linear OA(4110, 16431, F4, 19) (dual of [16431, 16321, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(4111, 16433, F4, 19) (dual of [16433, 16322, 20]-code) | [i] | ||
| 6 | Linear OA(4112, 16435, F4, 19) (dual of [16435, 16323, 20]-code) | [i] | ||
| 7 | Linear OOA(4109, 8214, F4, 2, 19) (dual of [(8214, 2), 16319, 20]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4109, 5476, F4, 3, 19) (dual of [(5476, 3), 16319, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(4109, 1825, F4, 19, 19) (dual of [(1825, 19), 34566, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |