MinT - Information on Result #1466736

Information on Result #1466736

Linear OOA(7¹⁰⁷, 55, F₇, 2, 96) (dual of [(55, 2), 3, 97]-NRT-code), using juxtaposition based on

linear OOA(7¹³, 8, F₇, 2, 13) (dual of [(8, 2), 3, 14]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;3,7) [i]
linear OOA(7⁹¹, 47, F₇, 2, 82) (dual of [(47, 2), 3, 83]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(7¹³, 8, F₇, 2, 13) (dual of [(8, 2), 3, 14]-NRT-code) (see above)
  2. linear OOA(7⁷⁵, 39, F₇, 2, 68) (dual of [(39, 2), 3, 69]-NRT-code), using
    - repeating each code word 3 times [i] based on linear OOA(7²³, 13, F₇, 2, 22) (dual of [(13, 2), 3, 23]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,3P) [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]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁹⁹, 51, F₇, 2, 88) (dual of [(51, 2), 3, 89]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(7⁹⁷, 50, F₇, 2, 86) (dual of [(50, 2), 3, 87]-NRT-code)	[i]		Truncation for OOAs