Information on Result #1541954
Linear OOA(4208, 43338, F4, 3, 33) (dual of [(43338, 3), 129806, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4208, 43338, F4, 33) (dual of [43338, 43130, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4208, 65591, F4, 33) (dual of [65591, 65383, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4206, 65589, F4, 33) (dual of [65589, 65383, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(413, 53, F4, 6) (dual of [53, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4206, 65589, F4, 33) (dual of [65589, 65383, 34]-code), using
Mode: 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 OOA(4208, 7222, F4, 39, 33) (dual of [(7222, 39), 281450, 34]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |