MinT - Information on Result #1118902

Information on Result #1118902

Linear OOA(256⁶⁷, 1678236, F₂₅₆, 5, 18) (dual of [(1678236, 5), 8391113, 19]-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(256⁵², 1677720, F₂₅₆, 5, 18) (dual of [(1677720, 5), 8388548, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(256⁵², 8388600, F₂₅₆, 18) (dual of [8388600, 8388548, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁵², large, F₂₅₆, 18) (dual of [large, large−52, 19]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.

Other Results with Identical Parameters

None.

Depending Results

None.