MinT - Information on Result #1027201

Information on Result #1027201

Linear OOA(4²⁰⁷, 72, F₄, 3, 164) (dual of [(72, 3), 9, 165]-NRT-code), using juxtaposition based on

linear OOA(4⁴⁵, 18, F₄, 3, 38) (dual of [(18, 3), 9, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁴⁵, 21, F₄, 3, 38) (dual of [(21, 3), 18, 39]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,24P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁵³, 54, F₄, 3, 125) (dual of [(54, 3), 9, 126]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(4⁷², 27, F₄, 3, 62) (dual of [(27, 3), 9, 63]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, 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(4²⁰⁷, 72, F₄, 3, 163) (dual of [(72, 3), 9, 164]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁰⁷, 72, F₄, 3, 162) (dual of [(72, 3), 9, 163]-NRT-code)	[i]		Strength Reduction for OOAs