MinT - Information on Result #2662632

Information on Result #2662632

Linear OOA(4¹²⁸, 44, F₄, 3, 111) (dual of [(44, 3), 4, 112]-NRT-code), using 6 step truncation based on linear OOA(4¹³⁴, 46, F₄, 3, 117) (dual of [(46, 3), 4, 118]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4²³, 9, F₄, 3, 22) (dual of [(9, 3), 4, 23]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
2. linear OOA(4¹⁰⁷, 37, F₄, 3, 94) (dual of [(37, 3), 4, 95]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4²³, 9, F₄, 3, 22) (dual of [(9, 3), 4, 23]-NRT-code) (see above)
    2. linear OOA(4⁸⁰, 28, F₄, 3, 71) (dual of [(28, 3), 4, 72]-NRT-code), using
      - repeating each code word 2 times [i] based on linear OOA(4³⁸, 14, F₄, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²⁶⁰, 88, F₄, 3, 223) (dual of [(88, 3), 4, 224]-NRT-code)	[i]		Repeating Each Code Word for NRT-Codes
2	Linear OOA(4¹⁴⁰, 48, F₄, 3, 120) (dual of [(48, 3), 4, 121]-NRT-code)	[i]		Juxtaposition for OOAs