MinT - Information on Result #1685820

Information on Result #1685820

Linear OOA(2²¹⁰, 2181, F₂, 7, 31) (dual of [(2181, 7), 15057, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁰, 2181, F₂, 3, 31) (dual of [(2181, 3), 6333, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹⁰, 2748, F₂, 3, 31) (dual of [(2748, 3), 8034, 32]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²⁰⁹, 2748, F₂, 3, 31) (dual of [(2748, 3), 8035, 32]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²⁰⁹, 8244, F₂, 31) (dual of [8244, 8035, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(24) [i] based on
      1. linear OA(2¹⁹⁶, 8192, F₂, 31) (dual of [8192, 7996, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(2¹⁵⁷, 8192, F₂, 25) (dual of [8192, 8035, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(2¹³, 52, F₂, 5) (dual of [52, 39, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³, 63, F₂, 5) (dual of [63, 50, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: 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.