MinT - Information on Result #909624

Information on Result #909624

Linear OOA(4¹⁴⁸, 77, F₄, 2, 111) (dual of [(77, 2), 6, 112]-NRT-code), using juxtaposition based on

linear OOA(4¹², 9, F₄, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
  - the Hermitian function field over F₄ [i]
linear OOA(4¹³⁰, 68, F₄, 2, 99) (dual of [(68, 2), 6, 100]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4²⁹, 17, F₄, 2, 24) (dual of [(17, 2), 5, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4³³, 17, F₄, 2, 33) (dual of [(17, 2), 1, 34]-NRT-code), using
    - dual of repetition NRT-code with length 17 [i]
  3. linear OOA(4³⁴, 17, F₄, 2, 34) (dual of [(17, 2), 0, 35]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4³⁴, 17, F₄, 2, 34) (dual of [(17, 2), 0, 35]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁶⁸, 87, F₄, 2, 124) (dual of [(87, 2), 6, 125]-NRT-code)	[i]		Juxtaposition for OOAs