Information on Result #1119295
Linear OOA(3221, 4866370, F3, 5, 14) (dual of [(4866370, 5), 24331629, 15]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(327, 1594322, F3, 5, 4) (dual of [(1594322, 5), 7971583, 5]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(327, 1594322, F3, 4, 4) (dual of [(1594322, 4), 6377261, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(327, 1594322, F3, 3, 4) (dual of [(1594322, 3), 4782939, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (23, 27, 1594322)-net over F3, using
- appending kth column [i] based on linear OOA(327, 1594322, F3, 3, 4) (dual of [(1594322, 3), 4782939, 5]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(327, 1594322, F3, 4, 4) (dual of [(1594322, 4), 6377261, 5]-NRT-code), using
- linear OOA(358, 1594328, F3, 5, 7) (dual of [(1594328, 5), 7971582, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(358, 4782985, F3, 7) (dual of [4782985, 4782927, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(358, 4782985, F3, 7) (dual of [4782985, 4782927, 8]-code), using
- linear OOA(3136, 1677720, F3, 5, 14) (dual of [(1677720, 5), 8388464, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3136, 8388600, F3, 14) (dual of [8388600, 8388464, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- OOA 5-folding [i] based on linear OA(3136, 8388600, F3, 14) (dual of [8388600, 8388464, 15]-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.