MinT - Information on Result #1052172

Information on Result #1052172

Linear OOA(2²³⁵, 2097173, F₂, 4, 18) (dual of [(2097173, 4), 8388457, 19]-NRT-code), using OOA 2-folding based on linear OOA(2²³⁵, 4194346, F₂, 2, 18) (dual of [(4194346, 2), 8388457, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁵, 4194347, F₂, 2, 18) (dual of [(4194347, 2), 8388459, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁸, 46, F₂, 2, 9) (dual of [(46, 2), 64, 10]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁹, 23, F₂, 2, 4) (dual of [(23, 2), 37, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 9, 23)-net over F₂, using
        linear code embedding found in a computer search [i]
      2. linear OOA(2¹⁹, 23, F₂, 2, 9) (dual of [(23, 2), 27, 10]-NRT-code), using
        extracting embedded OOA [i] based on digital (10, 19, 23)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²⁰⁷, 4194301, F₂, 2, 18) (dual of [(4194301, 2), 8388395, 19]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2²⁰⁷, 8388602, F₂, 18) (dual of [8388602, 8388395, 19]-code), using
      - discarding factors / shortening the dual code based on linear OA(2²⁰⁷, large, F₂, 18) (dual of [large, large−207, 19]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’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, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.