MinT - Information on Result #908661

Information on Result #908661

Linear OOA(2¹⁰⁸, 57, F₂, 2, 58) (dual of [(57, 2), 6, 59]-NRT-code), using juxtaposition based on

linear OOA(2⁶, 6, F₂, 2, 4) (dual of [(6, 2), 6, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2⁹⁶, 51, F₂, 2, 53) (dual of [(51, 2), 6, 54]-NRT-code), using
- repeating each code word 3 times [i] based on linear OOA(2²⁸, 17, F₂, 2, 17) (dual of [(17, 2), 6, 18]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
      - an explicit generator matrix by Edel [i]
    2. linear OOA(2¹⁷, 9, F₂, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
      - dual of repetition NRT-code with length 9 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹²⁴, 65, F₂, 2, 66) (dual of [(65, 2), 6, 67]-NRT-code)	[i]		Juxtaposition for OOAs