MinT - Information on Result #2631083

Information on Result #2631083

Linear OOA(4¹²⁵, 43, F₄, 3, 108) (dual of [(43, 3), 4, 109]-NRT-code), using strength reduction based on linear OOA(4¹²⁵, 43, F₄, 3, 109) (dual of [(43, 3), 4, 110]-NRT-code), using

juxtaposition [i] based on
1. 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]
2. linear OOA(4⁸³, 29, F₄, 3, 73) (dual of [(29, 3), 4, 74]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4³⁸, 14, F₄, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code) (see above)
    2. linear OOA(4⁴¹, 15, F₄, 3, 37) (dual of [(15, 3), 4, 38]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, 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(4²⁵⁴, 86, F₄, 3, 217) (dual of [(86, 3), 4, 218]-NRT-code)	[i]		Repeating Each Code Word for NRT-Codes
2	Linear OOA(4¹³⁷, 47, F₄, 3, 117) (dual of [(47, 3), 4, 118]-NRT-code)	[i]		Juxtaposition for OOAs