MinT - Information on Result #669757

Information on Result #669757

Linear OA(64⁶⁸, 4202, F₆₄, 26) (dual of [4202, 4134, 27]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁷, 106, F₆₄, 13) (dual of [106, 89, 14]-code), using
- constructionÂ X applied to AG(F,89P) âŠ‚ AG(F,91P) [i] based on
  1. linear OA(64¹⁶, 103, F₆₄, 13) (dual of [103, 87, 14]-code), using algebraic-geometric code AG(F,89P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64¹⁴, 103, F₆₄, 11) (dual of [103, 89, 12]-code), using algebraic-geometric code AG(F,91P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104 (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(64⁵¹, 4096, F₆₄, 26) (dual of [4096, 4045, 27]-code), using
- an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Mode: Constructive and linear.

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