MinT - Information on Result #904095

Information on Result #904095

Linear OOA(64⁸¹, 2226, F₆₄, 2, 30) (dual of [(2226, 2), 4371, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64²², 177, F₆₄, 2, 15) (dual of [(177, 2), 332, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,338P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(64⁵⁹, 2049, F₆₄, 2, 30) (dual of [(2049, 2), 4039, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁵⁹, 4098, F₆₄, 30) (dual of [4098, 4039, 31]-code), using
  - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
    1. linear OA(64⁵⁹, 4096, F₆₄, 30) (dual of [4096, 4037, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
    2. linear OA(64⁵⁷, 4096, F₆₄, 29) (dual of [4096, 4039, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

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