Information on Result #2446008
Linear OOA(4251, 4194399, F4, 2, 24) (dual of [(4194399, 2), 8388547, 25]-NRT-code), using strength reduction based on linear OOA(4251, 4194399, F4, 2, 25) (dual of [(4194399, 2), 8388547, 26]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(434, 98, F4, 2, 12) (dual of [(98, 2), 162, 13]-NRT-code), using
- extracting embedded OOA [i] based on digital (22, 34, 98)-net over F4, using
- trace code for nets [i] based on digital (5, 17, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- trace code for nets [i] based on digital (5, 17, 49)-net over F16, using
- extracting embedded OOA [i] based on digital (22, 34, 98)-net over F4, using
- linear OOA(4217, 4194301, F4, 2, 25) (dual of [(4194301, 2), 8388385, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4217, 8388602, F4, 25) (dual of [8388602, 8388385, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- OOA 2-folding [i] based on linear OA(4217, 8388602, F4, 25) (dual of [8388602, 8388385, 26]-code), using
- linear OOA(434, 98, F4, 2, 12) (dual of [(98, 2), 162, 13]-NRT-code), using
Mode: Constructive and 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
None.