MinT - Information on Result #1466715

Information on Result #1466715

Linear OOA(7⁷⁸, 41, F₇, 2, 68) (dual of [(41, 2), 4, 69]-NRT-code), using juxtaposition based on

linear OOA(7²², 13, F₇, 2, 21) (dual of [(13, 2), 4, 22]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₇ with g(F) = 1 and N(F) ≥ 13, using
  - sharp bound on the number of rational points on curves with genus 1 [i]
linear OOA(7⁵², 28, F₇, 2, 46) (dual of [(28, 2), 4, 47]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(7¹², 8, F₇, 2, 12) (dual of [(8, 2), 4, 13]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;4,7) [i]
  2. linear OOA(7³⁶, 20, F₇, 2, 33) (dual of [(20, 2), 4, 34]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₇ with g(F) = 3 and N(F) ≥ 20, using
      - fields by Serre with genus 3 or 4 [i]

Mode: Linear.

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