Information on Result #2950709
Linear OOA(2197, 1922387, F2, 7, 12) (dual of [(1922387, 7), 13456512, 13]-NRT-code), using strength reduction based on linear OOA(2197, 1922387, F2, 7, 13) (dual of [(1922387, 7), 13456512, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(258, 524287, F2, 7, 6) (dual of [(524287, 7), 3669951, 7]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(258, 524287, F2, 6, 6) (dual of [(524287, 6), 3145664, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(258, 524287, F2, 5, 6) (dual of [(524287, 5), 2621377, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F2, using
- 1 times m-reduction [i] based on digital (52, 59, 524287)-net over F2, using
- extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F2, using
- appending kth column [i] based on linear OOA(258, 524287, F2, 5, 6) (dual of [(524287, 5), 2621377, 7]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(258, 524287, F2, 6, 6) (dual of [(524287, 6), 3145664, 7]-NRT-code), using
- linear OOA(2139, 1398100, F2, 7, 13) (dual of [(1398100, 7), 9786561, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2139, 8388601, F2, 13) (dual of [8388601, 8388462, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2139, 8388601, F2, 13) (dual of [8388601, 8388462, 14]-code), using
- linear OOA(258, 524287, F2, 7, 6) (dual of [(524287, 7), 3669951, 7]-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.