Information on Result #678473
Linear OA(4164, 262199, F4, 23) (dual of [262199, 262035, 24]-code), using construction X applied to Ce(22) ⊂ Ce(16) based on
- linear OA(4154, 262144, F4, 23) (dual of [262144, 261990, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(4165, 262200, F4, 23) (dual of [262200, 262035, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4166, 262201, F4, 23) (dual of [262201, 262035, 24]-code) | [i] | ||
| 3 | Linear OA(4167, 262202, F4, 23) (dual of [262202, 262035, 24]-code) | [i] | ||
| 4 | Linear OA(4168, 262203, F4, 23) (dual of [262203, 262035, 24]-code) | [i] | ||
| 5 | Linear OA(4169, 262204, F4, 23) (dual of [262204, 262035, 24]-code) | [i] | ||
| 6 | Linear OA(4167, 262203, F4, 23) (dual of [262203, 262036, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(4168, 262205, F4, 23) (dual of [262205, 262037, 24]-code) | [i] | ||
| 8 | Linear OA(4169, 262207, F4, 23) (dual of [262207, 262038, 24]-code) | [i] | ||
| 9 | Linear OOA(4164, 131099, F4, 2, 23) (dual of [(131099, 2), 262034, 24]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(4164, 87399, F4, 3, 23) (dual of [(87399, 3), 262033, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(4164, 23836, F4, 23, 23) (dual of [(23836, 23), 548064, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |