MinT - Information on Result #1093707

Information on Result #1093707

Linear OOA(2²¹⁹, 56, F₂, 4, 168) (dual of [(56, 4), 5, 169]-NRT-code), using juxtaposition based on

linear OOA(2¹⁹, 6, F₂, 4, 17) (dual of [(6, 4), 5, 18]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,6P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁹⁵, 50, F₂, 4, 150) (dual of [(50, 4), 5, 151]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁵, 5, F₂, 4, 14) (dual of [(5, 4), 5, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁷⁵, 45, F₂, 4, 135) (dual of [(45, 4), 5, 136]-NRT-code), using
    - 2¹ times duplication [i] based on linear OOA(2¹⁷⁴, 45, F₂, 4, 135) (dual of [(45, 4), 6, 136]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        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]
        linear OOA(2¹⁷, 5, F₂, 4, 16) (dual of [(5, 4), 3, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5 (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁴³, 62, F₂, 4, 186) (dual of [(62, 4), 5, 187]-NRT-code)	[i]		Juxtaposition for OOAs
2	Linear OOA(2²¹⁹, 28, F₂, 8, 168) (dual of [(28, 8), 5, 169]-NRT-code)	[i]		OOA Folding