MinT - Information on Result #1049477

Information on Result #1049477

Linear OOA(2²²⁶, 77, F₂, 3, 161) (dual of [(77, 3), 5, 162]-NRT-code), using juxtaposition based on

linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;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]
linear OOA(2²¹¹, 72, F₂, 3, 151) (dual of [(72, 3), 5, 152]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²¹⁰, 72, F₂, 3, 151) (dual of [(72, 3), 6, 152]-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(2²¹, 8, F₂, 3, 18) (dual of [(8, 3), 3, 19]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2⁶, 3, F₂, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;3,2) [i]
        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 (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁶, 77, F₂, 3, 160) (dual of [(77, 3), 5, 161]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²²⁶, 77, F₂, 3, 159) (dual of [(77, 3), 5, 160]-NRT-code)	[i]		Strength Reduction for OOAs