Information on Result #679170
Linear OA(4116, 16422, F4, 21) (dual of [16422, 16306, 22]-code), using construction X applied to Ce(20) ⊂ Ce(14) 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(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(410, 38, F4, 5) (dual of [38, 28, 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(4117, 16423, F4, 21) (dual of [16423, 16306, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4118, 16424, F4, 21) (dual of [16424, 16306, 22]-code) | [i] | ||
| 3 | Linear OA(4115, 16421, F4, 20) (dual of [16421, 16306, 21]-code) | [i] | Truncation | |
| 4 | Linear OOA(4116, 8211, F4, 2, 21) (dual of [(8211, 2), 16306, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4116, 5474, F4, 3, 21) (dual of [(5474, 3), 16306, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(4116, 1642, F4, 21, 21) (dual of [(1642, 21), 34366, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |