MinT - Information on Result #2243915

Information on Result #2243915

Linear OA(4²⁵⁸, 339, F₄, 121) (dual of [339, 81, 122]-code), using 1 times truncation based on linear OA(4²⁵⁹, 340, F₄, 122) (dual of [340, 81, 123]-code), using

concatenation of two codes [i] based on
1. linear OA(64⁴¹, 68, F₆₄, 40) (dual of [68, 27, 41]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁴¹, 79, F₆₄, 40) (dual of [79, 38, 41]-code), using
    - algebraic-geometric code AG(F,38P) [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(4²⁶⁰, 341, F₄, 121) (dual of [341, 81, 122]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(4²⁵⁸, 169, F₄, 2, 121) (dual of [(169, 2), 80, 122]-NRT-code)	[i]	OOA Folding
3	Linear OOA(4²⁵⁸, 113, F₄, 3, 121) (dual of [(113, 3), 81, 122]-NRT-code)	[i]	OOA Folding