MinT - Information on Result #1475532

Information on Result #1475532

Linear OOA(4²⁵⁸, 132, F₄, 2, 205) (dual of [(132, 2), 6, 206]-NRT-code), using juxtaposition based on

linear OOA(4⁸, 7, F₄, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁸, 9, F₄, 2, 7) (dual of [(9, 2), 10, 8]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
linear OOA(4²⁴⁴, 125, F₄, 2, 197) (dual of [(125, 2), 6, 198]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16²², 25, F₁₆, 21) (dual of [25, 3, 22]-code), using
    - extended algebraic-geometric code AG_e(F,3P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 25, using
      - sharp bound on the number of rational points on curves with genus 1 [i]
  2. linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [i]

Mode: Linear.

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