MinT - Information on Result #2612660

Information on Result #2612660

Linear OOA(2¹³⁸, 76, F₂, 3, 48) (dual of [(76, 3), 90, 49]-NRT-code), using strength reduction based on linear OOA(2¹³⁸, 76, F₂, 3, 49) (dual of [(76, 3), 90, 50]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²⁷, 19, F₈, 3, 24) (dual of [(19, 3), 30, 25]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8²⁷, 24, F₈, 3, 24) (dual of [(24, 3), 45, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,47P) [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, 76, F₂, 3, 48) (dual of [(76, 3), 89, 49]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹³⁸, 38, F₂, 5, 48) (dual of [(38, 5), 52, 49]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2¹³⁸, 38, F₂, 6, 48) (dual of [(38, 6), 90, 49]-NRT-code)	[i]	OOA Folding