MinT - Information on Result #1049437

Information on Result #1049437

Linear OOA(2¹⁷⁴, 60, F₂, 3, 123) (dual of [(60, 3), 6, 124]-NRT-code), using juxtaposition based on

linear OOA(2¹⁸, 8, F₂, 3, 14) (dual of [(8, 3), 6, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,9P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁵⁰, 52, F₂, 3, 108) (dual of [(52, 3), 6, 109]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁵, 7, F₂, 3, 12) (dual of [(7, 3), 6, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹²⁹, 45, F₂, 3, 95) (dual of [(45, 3), 6, 96]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
        extended Reedâ€“Solomon code RS_e(2,8) [i]
        Simplex code S(2,8) [i]
      2. linear OOA(2¹², 5, F₂, 3, 11) (dual of [(5, 3), 3, 12]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁷³, 59, F₂, 3, 122) (dual of [(59, 3), 4, 123]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(2¹⁷⁴, 30, F₂, 6, 123) (dual of [(30, 6), 6, 124]-NRT-code)	[i]		OOA Folding