MinT - Information on Result #669932

Information on Result #669932

Linear OA(64⁵⁶, 262226, F₆₄, 16) (dual of [262226, 262170, 17]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁰, 82, F₆₄, 8) (dual of [82, 72, 9]-code), using
- constructionÂ X applied to AG(F,70P) âŠ‚ AG(F,72P) [i] based on
  1. linear OA(64⁹, 79, F₆₄, 8) (dual of [79, 70, 9]-code), using algebraic-geometric code AG(F,70P) [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(64⁷, 79, F₆₄, 6) (dual of [79, 72, 7]-code), using algebraic-geometric code AG(F,72P) [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(64⁴⁶, 262144, F₆₄, 16) (dual of [262144, 262098, 17]-code), using
- an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

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