MinT - Information on Result #941532

Information on Result #941532

Linear OOA(2¹¹¹, 59, F₂, 2, 66) (dual of [(59, 2), 7, 67]-NRT-code), using juxtaposition based on

linear OOA(2⁹, 8, F₂, 2, 6) (dual of [(8, 2), 7, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁹, 9, F₂, 2, 6) (dual of [(9, 2), 9, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (3, 9, 9)-net over F₂, using
    - a shift-net [i]
linear OOA(2⁹⁵, 51, F₂, 2, 59) (dual of [(51, 2), 7, 60]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2⁹⁴, 51, F₂, 2, 59) (dual of [(51, 2), 8, 60]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. 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(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹¹¹, 59, F₂, 2, 65) (dual of [(59, 2), 7, 66]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹¹¹, 59, F₂, 2, 64) (dual of [(59, 2), 7, 65]-NRT-code)	[i]		Strength Reduction for OOAs