MinT - Information on Result #669804

Information on Result #669804

Linear OA(64⁸⁸, 262274, F₆₄, 24) (dual of [262274, 262186, 25]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁸, 130, F₆₄, 12) (dual of [130, 112, 13]-code), using
- constructionÂ X applied to AG(F,114P) âŠ‚ AG(F,116P) [i] based on
  1. linear OA(64¹⁷, 127, F₆₄, 12) (dual of [127, 110, 13]-code), using algebraic-geometric code AG(F,114P) [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(64¹⁵, 127, F₆₄, 10) (dual of [127, 112, 11]-code), using algebraic-geometric code AG(F,116P) [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(64⁷⁰, 262144, F₆₄, 24) (dual of [262144, 262074, 25]-code), using
- an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Mode: Constructive and linear.

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