MinT - Information on Result #669836

Information on Result #669836

Linear OA(64⁶⁰, 4226, F₆₄, 22) (dual of [4226, 4166, 23]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁷, 130, F₆₄, 11) (dual of [130, 113, 12]-code), using
- constructionÂ X applied to AG(F,115P) âŠ‚ AG(F,117P) [i] based on
  1. linear OA(64¹⁶, 127, F₆₄, 11) (dual of [127, 111, 12]-code), using algebraic-geometric code AG(F,115P) [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64¹⁴, 127, F₆₄, 9) (dual of [127, 113, 10]-code), using algebraic-geometric code AG(F,117P) [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128 (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(64⁴³, 4096, F₆₄, 22) (dual of [4096, 4053, 23]-code), using
- an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Constructive and linear.

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