MinT - Information on Result #2208683

Information on Result #2208683

Linear OA(4²⁵⁷, 275, F₄, 162) (dual of [275, 18, 163]-code), using strength reduction based on linear OA(4²⁵⁷, 275, F₄, 163) (dual of [275, 18, 164]-code), using

concatenation of two codes [i] based on
1. linear OA(16⁴⁶, 55, F₁₆, 40) (dual of [55, 9, 41]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁴⁶, 64, F₁₆, 40) (dual of [64, 18, 41]-code), using
    - algebraic-geometric code AG(F,23P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]
2. linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
  - extended Reedâ€“Solomon code RS_e(2,4) [i]
  - Simplex code S(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(4²⁵⁶, 274, F₄, 161) (dual of [274, 18, 162]-code)	[i]	Truncation
2	Linear OA(4²⁵⁵, 273, F₄, 160) (dual of [273, 18, 161]-code)	[i]
3	Linear OA(4²⁵⁴, 272, F₄, 159) (dual of [272, 18, 160]-code)	[i]
4	Linear OA(4²⁵³, 271, F₄, 158) (dual of [271, 18, 159]-code)	[i]
5	Linear OA(4²⁵¹, 269, F₄, 156) (dual of [269, 18, 157]-code)	[i]