Information on Result #678245
Linear OA(4211, 1048636, F4, 27) (dual of [1048636, 1048425, 28]-code), using construction X applied to Ce(26) ⊂ Ce(20) based on
- linear OA(4201, 1048576, F4, 27) (dual of [1048576, 1048375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(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(4212, 1048637, F4, 27) (dual of [1048637, 1048425, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4213, 1048638, F4, 27) (dual of [1048638, 1048425, 28]-code) | [i] | ||
| 3 | Linear OA(4214, 1048639, F4, 27) (dual of [1048639, 1048425, 28]-code) | [i] | ||
| 4 | Linear OA(4215, 1048640, F4, 27) (dual of [1048640, 1048425, 28]-code) | [i] | ||
| 5 | Linear OA(4216, 1048641, F4, 27) (dual of [1048641, 1048425, 28]-code) | [i] | ||
| 6 | Linear OA(4215, 1048641, F4, 27) (dual of [1048641, 1048426, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(4216, 1048643, F4, 27) (dual of [1048643, 1048427, 28]-code) | [i] | ||
| 8 | Linear OOA(4211, 524318, F4, 2, 27) (dual of [(524318, 2), 1048425, 28]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(4211, 349545, F4, 3, 27) (dual of [(349545, 3), 1048424, 28]-NRT-code) | [i] | ||
| 10 | Linear OOA(4211, 80664, F4, 27, 27) (dual of [(80664, 27), 2177717, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |