Information on Result #1536133
Linear OOA(4117, 4194313, F4, 3, 13) (dual of [(4194313, 3), 12582822, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4117, 4194313, F4, 2, 13) (dual of [(4194313, 2), 8388509, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(48, 12, F4, 2, 6) (dual of [(12, 2), 16, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 8, 12)-net over F4, using
- linear OOA(4109, 4194301, F4, 2, 13) (dual of [(4194301, 2), 8388493, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4109, 8388602, F4, 13) (dual of [8388602, 8388493, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- OOA 2-folding [i] based on linear OA(4109, 8388602, F4, 13) (dual of [8388602, 8388493, 14]-code), using
- linear OOA(48, 12, F4, 2, 6) (dual of [(12, 2), 16, 7]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(4117, 2097156, F4, 15, 13) (dual of [(2097156, 15), 31457223, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |