MinT - Information on Result #941527

Information on Result #941527

Linear OOA(2¹⁰³, 55, F₂, 2, 60) (dual of [(55, 2), 7, 61]-NRT-code), using juxtaposition based on

linear OOA(2⁷, 7, F₂, 2, 5) (dual of [(7, 2), 7, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 7, 7)-net over F₂, using
  - a shift-net [i]
linear OOA(2⁸⁹, 48, F₂, 2, 54) (dual of [(48, 2), 7, 55]-NRT-code), using
- 5 step truncation [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(2¹⁰³, 55, F₂, 2, 59) (dual of [(55, 2), 7, 60]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁰³, 55, F₂, 2, 58) (dual of [(55, 2), 7, 59]-NRT-code)	[i]		Strength Reduction for OOAs