MinT - Information on Result #903663

Information on Result #903663

Linear OOA(64³², 2129, F₆₄, 2, 13) (dual of [(2129, 2), 4226, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64⁷, 80, F₆₄, 2, 6) (dual of [(80, 2), 153, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,153P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
  - a function field by SÃ©mirat [i]
linear OOA(64²⁵, 2049, F₆₄, 2, 13) (dual of [(2049, 2), 4073, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64²⁵, 4098, F₆₄, 13) (dual of [4098, 4073, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
    1. linear OA(64²⁵, 4096, F₆₄, 13) (dual of [4096, 4071, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(64²³, 4096, F₆₄, 12) (dual of [4096, 4073, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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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