MinT - Information on Result #1020079

Information on Result #1020079

Linear OOA(256³⁸, 22361, F₂₅₆, 3, 14) (dual of [(22361, 3), 67045, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹¹, 515, F₂₅₆, 3, 7) (dual of [(515, 3), 1534, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256³, 257, F₂₅₆, 3, 3) (dual of [(257, 3), 768, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;768,256) [i]
  2. linear OOA(256⁸, 258, F₂₅₆, 3, 7) (dual of [(258, 3), 766, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 8, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
linear OOA(256²⁷, 21846, F₂₅₆, 3, 14) (dual of [(21846, 3), 65511, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(256²⁷, 65538, F₂₅₆, 14) (dual of [65538, 65511, 15]-code), using
  - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
    1. linear OA(256²⁷, 65536, F₂₅₆, 14) (dual of [65536, 65509, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    2. linear OA(256²⁵, 65536, F₂₅₆, 13) (dual of [65536, 65511, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.