MinT - Information on Result #1118918

Information on Result #1118918

Linear OOA(256⁵², 13623, F₂₅₆, 5, 19) (dual of [(13623, 5), 68063, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁵, 516, F₂₅₆, 5, 9) (dual of [(516, 5), 2565, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁵, 258, F₂₅₆, 5, 4) (dual of [(258, 5), 1285, 5]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(256⁵, 258, F₂₅₆, 4, 4) (dual of [(258, 4), 1027, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(256⁵, 258, F₂₅₆, 3, 4) (dual of [(258, 3), 769, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (1, 5, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256¹⁰, 258, F₂₅₆, 5, 9) (dual of [(258, 5), 1280, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 10, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)
linear OOA(256³⁷, 13107, F₂₅₆, 5, 19) (dual of [(13107, 5), 65498, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(256³⁷, 65535, F₂₅₆, 19) (dual of [65535, 65498, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(256³⁷, 65536, F₂₅₆, 19) (dual of [65536, 65499, 20]-code), using
    - an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.