MinT - Information on Result #2286728

Information on Result #2286728

Linear OA(16¹²⁰, 4164, F₁₆, 35) (dual of [4164, 4044, 36]-code), using 1 times code embedding in larger space based on linear OA(16¹¹⁹, 4163, F₁₆, 35) (dual of [4163, 4044, 36]-code), using

constructionÂ X applied to C_e(34) âŠ‚ C_e(18) [i] based on
1. linear OA(16⁹⁷, 4096, F₁₆, 35) (dual of [4096, 3999, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
2. linear OA(16⁵², 4096, F₁₆, 19) (dual of [4096, 4044, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
3. linear OA(16²², 67, F₁₆, 15) (dual of [67, 45, 16]-code), using
  - constructionÂ X applied to AG(F,48P) âŠ‚ AG(F,50P) [i] based on
    1. linear OA(16²¹, 64, F₁₆, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [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(16¹⁹, 64, F₁₆, 13) (dual of [64, 45, 14]-code), using algebraic-geometric code AG(F,50P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 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		This result only	Method
1	Linear OOA(16¹²⁰, 2082, F₁₆, 2, 35) (dual of [(2082, 2), 4044, 36]-NRT-code)	[i]		OOA Folding