MinT - Information on Result #2631137

Information on Result #2631137

Linear OOA(4¹²⁷, 44, F₄, 3, 107) (dual of [(44, 3), 5, 108]-NRT-code), using strength reduction based on linear OOA(4¹²⁷, 44, F₄, 3, 108) (dual of [(44, 3), 5, 109]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4³⁷, 14, F₄, 3, 34) (dual of [(14, 3), 5, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,7P) [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(4⁸⁵, 30, F₄, 3, 73) (dual of [(30, 3), 5, 74]-NRT-code), using
  - repeating each code word 2 times [i] based on linear OOA(4⁴⁰, 15, F₄, 3, 36) (dual of [(15, 3), 5, 37]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,8P) [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(4²⁵⁹, 88, F₄, 3, 215) (dual of [(88, 3), 5, 216]-NRT-code)	[i]		Repeating Each Code Word for NRT-Codes