Information on Result #678469
Linear OA(4191, 262199, F4, 27) (dual of [262199, 262008, 28]-code), using construction X applied to Ce(26) ⊂ Ce(20) based on
- linear OA(4181, 262144, F4, 27) (dual of [262144, 261963, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(410, 55, F4, 5) (dual of [55, 45, 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(4192, 262200, F4, 27) (dual of [262200, 262008, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4193, 262201, F4, 27) (dual of [262201, 262008, 28]-code) | [i] | ||
| 3 | Linear OA(4194, 262202, F4, 27) (dual of [262202, 262008, 28]-code) | [i] | ||
| 4 | Linear OA(4195, 262203, F4, 27) (dual of [262203, 262008, 28]-code) | [i] | ||
| 5 | Linear OA(4196, 262204, F4, 27) (dual of [262204, 262008, 28]-code) | [i] | ||
| 6 | Linear OA(4194, 262203, F4, 27) (dual of [262203, 262009, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(4195, 262205, F4, 27) (dual of [262205, 262010, 28]-code) | [i] | ||
| 8 | Linear OA(4196, 262207, F4, 27) (dual of [262207, 262011, 28]-code) | [i] | ||
| 9 | Linear OOA(4191, 131099, F4, 2, 27) (dual of [(131099, 2), 262007, 28]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(4191, 87399, F4, 3, 27) (dual of [(87399, 3), 262006, 28]-NRT-code) | [i] | ||
| 11 | Linear OOA(4191, 20169, F4, 27, 27) (dual of [(20169, 27), 544372, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |