MinT - Information on Result #941525

Information on Result #941525

Linear OOA(2¹¹⁴, 61, F₂, 2, 68) (dual of [(61, 2), 8, 69]-NRT-code), using juxtaposition based on

linear OOA(2¹², 10, F₂, 2, 8) (dual of [(10, 2), 8, 9]-NRT-code), using
- an explicit generator matrix by Edel [i]
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		Method
1	Linear OOA(2¹¹⁴, 61, F₂, 2, 67) (dual of [(61, 2), 8, 68]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹¹⁴, 61, F₂, 2, 66) (dual of [(61, 2), 8, 67]-NRT-code)	[i]
3	Linear OOA(2¹¹⁴, 61, F₂, 2, 65) (dual of [(61, 2), 8, 66]-NRT-code)	[i]
4	Linear OOA(2¹¹⁴, 61, F₂, 2, 64) (dual of [(61, 2), 8, 65]-NRT-code)	[i]
5	Linear OOA(2¹¹⁶, 62, F₂, 2, 68) (dual of [(62, 2), 8, 69]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
6	Linear OOA(2¹¹⁵, 61, F₂, 2, 68) (dual of [(61, 2), 7, 69]-NRT-code)	[i]	OOA Duplication
7	Linear OOA(2¹¹³, 60, F₂, 2, 67) (dual of [(60, 2), 7, 68]-NRT-code)	[i]	Truncation for OOAs