MinT - Information on Result #909736

Information on Result #909736

Linear OOA(4¹⁷⁵, 90, F₄, 2, 133) (dual of [(90, 2), 5, 134]-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(4¹⁵⁷, 81, F₄, 2, 120) (dual of [(81, 2), 5, 121]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code) (see above)
  2. 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
        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 (see above)
        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]
        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]
        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(4¹⁷⁵, 90, F₄, 2, 132) (dual of [(90, 2), 5, 133]-NRT-code)	[i]		Strength Reduction for OOAs