Information on Result #678240
Linear OA(4251, 1048636, F4, 32) (dual of [1048636, 1048385, 33]-code), using construction X applied to Ce(32) ⊂ Ce(25) based on
- linear OA(4241, 1048576, F4, 33) (dual of [1048576, 1048335, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4191, 1048576, F4, 26) (dual of [1048576, 1048385, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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 OA(4252, 1048637, F4, 32) (dual of [1048637, 1048385, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4251, 524318, F4, 2, 32) (dual of [(524318, 2), 1048385, 33]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4251, 349545, F4, 3, 32) (dual of [(349545, 3), 1048384, 33]-NRT-code) | [i] | ||