MinT - Information on Result #1027572

Information on Result #1027572

Linear OOA(4¹⁴⁷, 50, F₄, 3, 132) (dual of [(50, 3), 3, 133]-NRT-code), using juxtaposition based on

linear OOA(4¹², 5, F₄, 3, 12) (dual of [(5, 3), 3, 13]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;3,4) [i]
linear OOA(4¹³², 45, F₄, 3, 119) (dual of [(45, 3), 3, 120]-NRT-code), using
- repeating each code word 5 times [i] based on linear OOA(4²⁴, 9, F₄, 3, 23) (dual of [(9, 3), 3, 24]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,3P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [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(4¹⁴⁷, 50, F₄, 3, 131) (dual of [(50, 3), 3, 132]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹⁴⁷, 50, F₄, 3, 130) (dual of [(50, 3), 3, 131]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(4¹⁴⁵, 49, F₄, 3, 130) (dual of [(49, 3), 2, 131]-NRT-code)	[i]		Truncation for OOAs
4	Linear OOA(4¹³⁹, 47, F₄, 3, 124) (dual of [(47, 3), 2, 125]-NRT-code)	[i]
5	Linear OOA(4¹³⁶, 46, F₄, 3, 121) (dual of [(46, 3), 2, 122]-NRT-code)	[i]
6	Linear OOA(4¹²⁹, 44, F₄, 3, 114) (dual of [(44, 3), 3, 115]-NRT-code)	[i]
7	Linear OOA(4¹²⁷, 43, F₄, 3, 112) (dual of [(43, 3), 2, 113]-NRT-code)	[i]
8	Linear OOA(4¹²⁶, 43, F₄, 3, 111) (dual of [(43, 3), 3, 112]-NRT-code)	[i]
9	Linear OOA(4¹²³, 42, F₄, 3, 108) (dual of [(42, 3), 3, 109]-NRT-code)	[i]
10	Linear OOA(4¹⁶², 55, F₄, 3, 145) (dual of [(55, 3), 3, 146]-NRT-code)	[i]		Juxtaposition for OOAs