Information on Result #2495365
Linear OOA(4173, 4194541, F4, 2, 17) (dual of [(4194541, 2), 8388909, 18]-NRT-code), using 41 times duplication based on linear OOA(4172, 4194541, F4, 2, 17) (dual of [(4194541, 2), 8388910, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(427, 240, F4, 2, 8) (dual of [(240, 2), 453, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (19, 27, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 9, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 9, 80)-net over F64, using
- extracting embedded OOA [i] based on digital (19, 27, 240)-net over F4, using
- linear OOA(4145, 4194301, F4, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- linear OOA(427, 240, F4, 2, 8) (dual of [(240, 2), 453, 9]-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.