MinT - Information on Result #2612659

Information on Result #2612659

Linear OOA(2¹³⁸, 72, F₂, 3, 50) (dual of [(72, 3), 78, 51]-NRT-code), using strength reduction based on linear OOA(2¹³⁸, 72, F₂, 3, 51) (dual of [(72, 3), 78, 52]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²⁸, 18, F₈, 3, 25) (dual of [(18, 3), 26, 26]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8²⁸, 24, F₈, 3, 25) (dual of [(24, 3), 44, 26]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,46P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]
2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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		Method
1	Linear OOA(2¹³⁹, 72, F₂, 3, 50) (dual of [(72, 3), 77, 51]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹³⁸, 36, F₂, 5, 50) (dual of [(36, 5), 42, 51]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2¹³⁸, 36, F₂, 6, 50) (dual of [(36, 6), 78, 51]-NRT-code)	[i]	OOA Folding