MinT - Information on Result #909738

Information on Result #909738

Linear OOA(4²⁰⁵, 105, F₄, 2, 156) (dual of [(105, 2), 5, 157]-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(4¹⁸⁷, 96, F₄, 2, 143) (dual of [(96, 2), 5, 144]-NRT-code), using
- repeating each code word 3 times [i] based on linear OOA(4⁵⁹, 32, F₄, 2, 47) (dual of [(32, 2), 5, 48]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. 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 (see above)
    2. linear OOA(4¹⁵, 8, F₄, 2, 15) (dual of [(8, 2), 1, 16]-NRT-code), using
      - dual of repetition NRT-code with length 8 [i]
    3. linear OOA(4¹⁶, 8, F₄, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4¹⁶, 8, F₄, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²⁰⁵, 105, F₄, 2, 155) (dual of [(105, 2), 5, 156]-NRT-code)	[i]		Strength Reduction for OOAs