MinT - Information on Result #661797

Information on Result #661797

Linear OA(2²⁵⁵, 282, F₂, 107) (dual of [282, 27, 108]-code), using constructionÂ X applied to C₂ âŠ‚ C₁ based on

linear OA(2²³⁵, 255, F₂, 111) (dual of [255, 20, 112]-code), using code C₂ for uÂ =Â 8 by de Boer and Brouwer [i]
linear OA(2²²⁷, 255, F₂, 95) (dual of [255, 28, 96]-code), using code C₁ for uÂ =Â 8 by de Boer and Brouwer [i]
linear OA(2²⁰, 27, F₂, 11) (dual of [27, 7, 12]-code), using
- residual code [i] based on linear OA(2⁴³, 51, F₂, 23) (dual of [51, 8, 24]-code), using
  - concatenation of two 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 OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁵⁵, 141, F₂, 2, 107) (dual of [(141, 2), 27, 108]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁵⁵, 94, F₂, 3, 107) (dual of [(94, 3), 27, 108]-NRT-code)	[i]		OOA Folding