MinT - Information on Result #909841

Information on Result #909841

Linear OOA(4⁹⁶, 50, F₄, 2, 77) (dual of [(50, 2), 4, 78]-NRT-code), using juxtaposition based on

linear OOA(4¹², 8, F₄, 2, 11) (dual of [(8, 2), 4, 12]-NRT-code), using
- discarding factors / shortening the dual code 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(4⁸⁰, 42, F₄, 2, 65) (dual of [(42, 2), 4, 66]-NRT-code), using
- repeating each code word 3 times [i] based on linear OOA(4²⁴, 14, F₄, 2, 21) (dual of [(14, 2), 4, 22]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹¹², 58, F₄, 2, 89) (dual of [(58, 2), 4, 90]-NRT-code)	[i]		Juxtaposition for OOAs
2	Linear OOA(4¹¹⁴, 59, F₄, 2, 91) (dual of [(59, 2), 4, 92]-NRT-code)	[i]		Juxtaposition for OOAs