MinT - Information on Result #2417291

Information on Result #2417291

Linear OOA(2⁶⁸, 60, F₂, 2, 22) (dual of [(60, 2), 52, 23]-NRT-code), using strength reduction based on linear OOA(2⁶⁸, 60, F₂, 2, 23) (dual of [(60, 2), 52, 24]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16¹¹, 12, F₁₆, 2, 11) (dual of [(12, 2), 13, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16¹¹, 16, F₁₆, 2, 11) (dual of [(16, 2), 21, 12]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;21,16) [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2⁶⁸, 30, F₂, 4, 22) (dual of [(30, 4), 52, 23]-NRT-code)	[i]		OOA Folding