MinT - Information on Result #2417129

Information on Result #2417129

Linear OOA(2⁶¹, 56, F₂, 2, 20) (dual of [(56, 2), 51, 21]-NRT-code), using strength reduction based on linear OOA(2⁶¹, 56, F₂, 2, 21) (dual of [(56, 2), 51, 22]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8¹¹, 14, F₈, 2, 10) (dual of [(14, 2), 17, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,17P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [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		This result only	Method
1	Linear OOA(2⁶², 56, F₂, 2, 20) (dual of [(56, 2), 50, 21]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2⁶¹, 28, F₂, 4, 20) (dual of [(28, 4), 51, 21]-NRT-code)	[i]		OOA Folding