MinT - Information on Result #2208791

Information on Result #2208791

Linear OA(4²⁵⁸, 360, F₄, 112) (dual of [360, 102, 113]-code), using strength reduction based on linear OA(4²⁵⁸, 360, F₄, 113) (dual of [360, 102, 114]-code), using

concatenation of two codes [i] based on
1. linear OA(64³⁸, 72, F₆₄, 37) (dual of [72, 34, 38]-code), using
  - discarding factors / shortening the dual code based on linear OA(64³⁸, 79, F₆₄, 37) (dual of [79, 41, 38]-code), using
    - algebraic-geometric code AG(F,41P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
2. linear OA(4², 5, F₄, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
  - extended Reedâ€“Solomon code RS_e(3,4) [i]
  - Hamming code H(2,4) [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 OA(4²⁵⁷, 359, F₄, 111) (dual of [359, 102, 112]-code)	[i]	Truncation
2	Linear OOA(4²⁵⁸, 180, F₄, 2, 112) (dual of [(180, 2), 102, 113]-NRT-code)	[i]	OOA Folding
3	Linear OOA(4²⁵⁸, 120, F₄, 3, 112) (dual of [(120, 3), 102, 113]-NRT-code)	[i]	OOA Folding