MinT - Information on Result #1093691

Information on Result #1093691

Linear OOA(2²⁴², 62, F₂, 4, 184) (dual of [(62, 4), 6, 185]-NRT-code), using juxtaposition based on

linear OOA(2³⁰, 9, F₂, 4, 25) (dual of [(9, 4), 6, 26]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2²⁰⁶, 53, F₂, 4, 158) (dual of [(53, 4), 6, 159]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2²⁶, 8, F₂, 4, 22) (dual of [(8, 4), 6, 23]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;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]
  2. linear OOA(2¹⁷⁴, 45, F₂, 4, 135) (dual of [(45, 4), 6, 136]-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(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, 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(2²⁴², 62, F₂, 4, 183) (dual of [(62, 4), 6, 184]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁴², 31, F₂, 8, 184) (dual of [(31, 8), 6, 185]-NRT-code)	[i]		OOA Folding