MinT - Information on Result #894657

Information on Result #894657

Linear OOA(2¹⁰⁹, 58, F₂, 2, 57) (dual of [(58, 2), 7, 58]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵², 29, F₂, 2, 28) (dual of [(29, 2), 6, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁵², 30, F₂, 2, 28) (dual of [(30, 2), 8, 29]-NRT-code), using
  - strength reduction [i] based on linear OOA(2⁵², 30, F₂, 2, 29) (dual of [(30, 2), 8, 30]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(4¹¹, 15, F₄, 9) (dual of [15, 4, 10]-code), using
        2 times truncation [i] based on linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
        projective code from ovoid in PG(3,Â 4) [i]
      2. linear OOA(2², 2, F₂, 2, 2) (dual of [(2, 2), 2, 3]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;2,2) [i]
linear OOA(2⁵⁷, 29, F₂, 2, 57) (dual of [(29, 2), 1, 58]-NRT-code), using
- dual of repetition NRT-code with length 29 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁴, 116, F₂, 2, 115) (dual of [(116, 2), 8, 116]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs