MinT - Information on Result #1027402

Information on Result #1027402

Linear OOA(4²¹⁰, 72, F₄, 3, 174) (dual of [(72, 3), 6, 175]-NRT-code), using juxtaposition based on

linear OOA(4⁴⁵, 17, F₄, 3, 40) (dual of [(17, 3), 6, 41]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁵⁹, 55, F₄, 3, 133) (dual of [(55, 3), 6, 134]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4³⁶, 14, F₄, 3, 33) (dual of [(14, 3), 6, 34]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4¹¹⁷, 41, F₄, 3, 99) (dual of [(41, 3), 6, 100]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(4³⁶, 14, F₄, 3, 33) (dual of [(14, 3), 6, 34]-NRT-code) (see above)
      2. linear OOA(4⁷⁵, 27, F₄, 3, 65) (dual of [(27, 3), 6, 66]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,15P) [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(4²⁰³, 69, F₄, 3, 167) (dual of [(69, 3), 4, 168]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(4²⁰², 69, F₄, 3, 166) (dual of [(69, 3), 5, 167]-NRT-code)	[i]		Truncation for OOAs