MinT - Information on Result #904055

Information on Result #904055

Linear OOA(64⁷⁶, 2226, F₆₄, 2, 28) (dual of [(2226, 2), 4376, 29]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64²¹, 177, F₆₄, 2, 14) (dual of [(177, 2), 333, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,339P) [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(64⁵⁵, 2049, F₆₄, 2, 28) (dual of [(2049, 2), 4043, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁵⁵, 4098, F₆₄, 28) (dual of [4098, 4043, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
    1. linear OA(64⁵⁵, 4096, F₆₄, 28) (dual of [4096, 4041, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(64⁵³, 4096, F₆₄, 27) (dual of [4096, 4043, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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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