MinT - Information on Result #2275527

Information on Result #2275527

Linear OA(4²³⁷, 336, F₄, 101) (dual of [336, 99, 102]-code), using 1 times code embedding in larger space based on linear OA(4²³⁶, 335, F₄, 101) (dual of [335, 99, 102]-code), using

concatenation of two codes [i] based on
1. linear OA(64³⁴, 67, F₆₄, 33) (dual of [67, 33, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(64³⁴, 79, F₆₄, 33) (dual of [79, 45, 34]-code), using
    - algebraic-geometric code AG(F,45P) [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		This result only	Method
1	Linear OOA(4²³⁷, 168, F₄, 2, 101) (dual of [(168, 2), 99, 102]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4²³⁷, 112, F₄, 3, 101) (dual of [(112, 3), 99, 102]-NRT-code)	[i]		OOA Folding