MinT - Information on Result #1673151

Information on Result #1673151

Linear OOA(256⁶², 15413, F₂₅₆, 6, 30) (dual of [(15413, 6), 92416, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶², 15413, F₂₅₆, 4, 30) (dual of [(15413, 4), 61590, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶², 16386, F₂₅₆, 4, 30) (dual of [(16386, 4), 65482, 31]-NRT-code), using
- 256¹ times duplication [i] based on linear OOA(256⁶¹, 16386, F₂₅₆, 4, 30) (dual of [(16386, 4), 65483, 31]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(256⁶¹, 65544, F₂₅₆, 30) (dual of [65544, 65483, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(26) [i] based on
      1. linear OA(256⁵⁹, 65536, F₂₅₆, 30) (dual of [65536, 65477, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(256⁵³, 65536, F₂₅₆, 27) (dual of [65536, 65483, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      3. linear OA(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
        discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
        Reedâ€“Solomon code RS(254,256) [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.