Information on Result #678738
Linear OA(4131, 65578, F4, 21) (dual of [65578, 65447, 22]-code), using construction X applied to Ce(20) ⊂ Ce(14) based on
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(4132, 65579, F4, 21) (dual of [65579, 65447, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4133, 65580, F4, 21) (dual of [65580, 65447, 22]-code) | [i] | ||
| 3 | Linear OA(4130, 65577, F4, 20) (dual of [65577, 65447, 21]-code) | [i] | Truncation | |
| 4 | Linear OOA(4131, 32789, F4, 2, 21) (dual of [(32789, 2), 65447, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4131, 21859, F4, 3, 21) (dual of [(21859, 3), 65446, 22]-NRT-code) | [i] | ||