MinT - Information on Result #1093683

Information on Result #1093683

Linear OOA(2²⁵⁸, 66, F₂, 4, 195) (dual of [(66, 4), 6, 196]-NRT-code), using juxtaposition based on

linear OOA(2²², 7, F₂, 4, 19) (dual of [(7, 4), 6, 20]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;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]
linear OOA(2²³⁰, 59, F₂, 4, 175) (dual of [(59, 4), 6, 176]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2²², 7, F₂, 4, 19) (dual of [(7, 4), 6, 20]-NRT-code) (see above)
  2. linear OOA(2²⁰², 52, F₂, 4, 155) (dual of [(52, 4), 6, 156]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2²², 7, F₂, 4, 19) (dual of [(7, 4), 6, 20]-NRT-code) (see above)
      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
        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, 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(2²⁵⁸, 66, F₂, 4, 194) (dual of [(66, 4), 6, 195]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁵⁸, 33, F₂, 8, 195) (dual of [(33, 8), 6, 196]-NRT-code)	[i]		OOA Folding