MinT - Information on Result #2479641

Information on Result #2479641

Linear OOA(2⁷⁸, 57, F₂, 2, 30) (dual of [(57, 2), 36, 31]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2⁷⁶, 56, F₂, 2, 30) (dual of [(56, 2), 36, 31]-NRT-code), using

strength reduction [i] based on linear OOA(2⁷⁶, 56, F₂, 2, 31) (dual of [(56, 2), 36, 32]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(8¹⁶, 14, F₈, 2, 15) (dual of [(14, 2), 12, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,12P) [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(2⁷⁹, 57, F₂, 2, 30) (dual of [(57, 2), 35, 31]-NRT-code)	[i]		OOA Duplication