Information on Result #678585
Linear OA(4107, 65579, F4, 17) (dual of [65579, 65472, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(465, 65537, F4, 11) (dual of [65537, 65472, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(410, 42, F4, 5) (dual of [42, 32, 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(4108, 65580, F4, 17) (dual of [65580, 65472, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4106, 65578, F4, 16) (dual of [65578, 65472, 17]-code) | [i] | Truncation | |
| 3 | Linear OOA(4107, 32789, F4, 2, 17) (dual of [(32789, 2), 65471, 18]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4107, 21859, F4, 3, 17) (dual of [(21859, 3), 65470, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(4107, 8197, F4, 17, 17) (dual of [(8197, 17), 139242, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |