MinT - Information on Result #3267723

Information on Result #3267723

Digital (48, 69, 209718)-net over F₁₂₈, using 128¹ times duplication based on digital (47, 68, 209718)-net over F₁₂₈, using

net defined by OOA [i] based on linear OOA(128⁶⁸, 209718, F₁₂₈, 21, 21) (dual of [(209718, 21), 4404010, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(128⁶⁸, 2097181, F₁₂₈, 21) (dual of [2097181, 2097113, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁶⁸, 2097184, F₁₂₈, 21) (dual of [2097184, 2097116, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(128⁶¹, 2097153, F₁₂₈, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(128³⁷, 2097153, F₁₂₈, 13) (dual of [2097153, 2097116, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(128⁷, 31, F₁₂₈, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
        discarding factors / shortening the dual code based on linear OA(128⁷, 128, F₁₂₈, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
        Reedâ€“Solomon code RS(121,128) [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.