MinT - Information on Result #909748

Information on Result #909748

Linear OOA(4¹⁶⁵, 85, F₄, 2, 126) (dual of [(85, 2), 5, 127]-NRT-code), using juxtaposition based on

linear OOA(4²¹, 13, F₄, 2, 18) (dual of [(13, 2), 5, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²¹, 14, F₄, 2, 18) (dual of [(14, 2), 7, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹³⁹, 72, F₄, 2, 107) (dual of [(72, 2), 5, 108]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(4⁶⁷, 36, F₄, 2, 53) (dual of [(36, 2), 5, 54]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4¹⁴, 9, F₄, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
    2. linear OOA(4¹⁷, 9, F₄, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
      - dual of repetition NRT-code with length 9 [i]
    3. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁹³, 99, F₄, 2, 147) (dual of [(99, 2), 5, 148]-NRT-code)	[i]		Juxtaposition for OOAs