Information on Result #823615
Linear OOA(4161, 524318, F4, 2, 20) (dual of [(524318, 2), 1048475, 21]-NRT-code), using OOA 2-folding based on linear OA(4161, 1048636, F4, 20) (dual of [1048636, 1048475, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4101, 1048576, F4, 14) (dual of [1048576, 1048475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(410, 60, F4, 5) (dual of [60, 50, 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(4163, 524319, F4, 2, 20) (dual of [(524319, 2), 1048475, 21]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4162, 524318, F4, 2, 20) (dual of [(524318, 2), 1048474, 21]-NRT-code) | [i] | OOA Duplication | |