MinT - Information on Result #2617111

Information on Result #2617111

Linear OOA(2²¹⁶, 132, F₂, 3, 64) (dual of [(132, 3), 180, 65]-NRT-code), using strength reduction based on linear OOA(2²¹⁶, 132, F₂, 3, 65) (dual of [(132, 3), 180, 66]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8³⁹, 33, F₈, 3, 32) (dual of [(33, 3), 60, 33]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8³⁹, 34, F₈, 3, 32) (dual of [(34, 3), 63, 33]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,69P) [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [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(2²¹⁷, 132, F₂, 3, 64) (dual of [(132, 3), 179, 65]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²¹⁶, 66, F₂, 5, 64) (dual of [(66, 5), 114, 65]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2²¹⁶, 66, F₂, 6, 64) (dual of [(66, 6), 180, 65]-NRT-code)	[i]	OOA Folding