MinT - Information on Result #909730

Information on Result #909730

Linear OOA(4¹⁴¹, 73, F₄, 2, 108) (dual of [(73, 2), 5, 109]-NRT-code), using juxtaposition based on

linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(4¹²³, 64, F₄, 2, 95) (dual of [(64, 2), 5, 96]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4²⁸, 16, F₄, 2, 23) (dual of [(16, 2), 4, 24]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4²⁸, 17, F₄, 2, 23) (dual of [(17, 2), 6, 24]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(4³¹, 16, F₄, 2, 31) (dual of [(16, 2), 1, 32]-NRT-code), using
    - dual of repetition NRT-code with length 16 [i]
  3. linear OOA(4³², 16, F₄, 2, 32) (dual of [(16, 2), 0, 33]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4³², 16, F₄, 2, 32) (dual of [(16, 2), 0, 33]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁴¹, 73, F₄, 2, 107) (dual of [(73, 2), 5, 108]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹⁶⁹, 87, F₄, 2, 129) (dual of [(87, 2), 5, 130]-NRT-code)	[i]		Juxtaposition for OOAs