MinT - Information on Result #1204776

Information on Result #1204776

Digital (28, 46, 7368)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁴⁶, 7368, F₂₅₆, 21, 18) (dual of [(7368, 21), 154682, 19]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(256⁴⁶, 22105, F₂₅₆, 3, 18) (dual of [(22105, 3), 66269, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256¹¹, 259, F₂₅₆, 3, 9) (dual of [(259, 3), 766, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 11, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256³⁵, 21846, F₂₅₆, 3, 18) (dual of [(21846, 3), 65503, 19]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(256³⁵, 65538, F₂₅₆, 18) (dual of [65538, 65503, 19]-code), using
      - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
        linear OA(256³⁵, 65536, F₂₅₆, 18) (dual of [65536, 65501, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
        linear OA(256³³, 65536, F₂₅₆, 17) (dual of [65536, 65503, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.