MinT - Information on Result #669825

Information on Result #669825

Linear OA(64⁸⁴, 262275, F₆₄, 23) (dual of [262275, 262191, 24]-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(64⁶⁷, 262145, F₆₄, 23) (dual of [262145, 262078, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]

Mode: Constructive and linear.

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