MinT - Information on Result #669624

Information on Result #669624

Linear OA(64⁹¹, 4178, F₆₄, 36) (dual of [4178, 4087, 37]-code), using (u,Â u+v)-construction based on

linear OA(64²⁰, 82, F₆₄, 18) (dual of [82, 62, 19]-code), using
- constructionÂ X applied to AG(F,60P) âŠ‚ AG(F,62P) [i] based on
  1. linear OA(64¹⁹, 79, F₆₄, 18) (dual of [79, 60, 19]-code), using algebraic-geometric code AG(F,60P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64¹⁷, 79, F₆₄, 16) (dual of [79, 62, 17]-code), using algebraic-geometric code AG(F,62P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80 (see above)
  3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(64⁷¹, 4096, F₆₄, 36) (dual of [4096, 4025, 37]-code), using
- an extension C_e(35) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,35], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]

Mode: Constructive and linear.

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