Information on Result #737148
Linear OA(4199, 4194370, F4, 23) (dual of [4194370, 4194171, 24]-code), using construction X applied to Ce(22) ⊂ Ce(16) based on
- linear OA(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(411, 66, F4, 5) (dual of [66, 55, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(411, 68, F4, 5) (dual of [68, 57, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(47, 64, F4, 3) (dual of [64, 57, 4]-code or 64-cap in PG(6,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(411, 68, F4, 5) (dual of [68, 57, 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(4201, 4194372, F4, 23) (dual of [4194372, 4194171, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4202, 4194373, F4, 23) (dual of [4194373, 4194171, 24]-code) | [i] | ||
| 3 | Linear OA(4203, 4194374, F4, 23) (dual of [4194374, 4194171, 24]-code) | [i] | ||
| 4 | Linear OA(4204, 4194375, F4, 23) (dual of [4194375, 4194171, 24]-code) | [i] | ||
| 5 | Linear OA(4204, 4194378, F4, 23) (dual of [4194378, 4194174, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4199, 2097185, F4, 2, 23) (dual of [(2097185, 2), 4194171, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4199, 1398123, F4, 3, 23) (dual of [(1398123, 3), 4194170, 24]-NRT-code) | [i] | ||