MinT - Information on Result #2174897

Information on Result #2174897

Linear OA(2⁶⁵, 79, F₂, 29) (dual of [79, 14, 30]-code), using adding a parity check bit based on linear OA(2⁶⁴, 78, F₂, 28) (dual of [78, 14, 29]-code), using

residual code [i] based on linear OA(2¹²¹, 136, F₂, 57) (dual of [136, 15, 58]-code), using
- adding a parity check bit [i] based on linear OA(2¹²⁰, 135, F₂, 56) (dual of [135, 15, 57]-code), using
  - constructionÂ X applied to D₃ âŠ‚ D₂ [i] based on
    1. linear OA(2¹¹⁹, 127, F₂, 58) (dual of [127, 8, 59]-code), using augmented code D₃ for uÂ =Â 7 by de Boer and Brouwer [i]
    2. linear OA(2¹¹², 127, F₂, 54) (dual of [127, 15, 55]-code), using augmented code D₂ for uÂ =Â 7 by de Boer and Brouwer [i]
    3. linear OA(2¹, 8, F₂, 1) (dual of [8, 7, 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(2³⁶, 49, F₂, 14) (dual of [49, 13, 15]-code)	[i]	Residual Code
2	Linear OOA(2⁶⁵, 39, F₂, 2, 29) (dual of [(39, 2), 13, 30]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2⁶⁵, 26, F₂, 3, 29) (dual of [(26, 3), 13, 30]-NRT-code)	[i]	OOA Folding