MinT - Information on Result #732024

Information on Result #732024

Linear OA(16¹⁰⁴, 4170, F₁₆, 29) (dual of [4170, 4066, 30]-code), using (u,Â u+v)-construction based on

linear OA(16²¹, 67, F₁₆, 14) (dual of [67, 46, 15]-code), using
- constructionÂ X applied to AG(F,49P) âŠ‚ AG(F,51P) [i] based on
  1. linear OA(16²⁰, 64, F₁₆, 14) (dual of [64, 44, 15]-code), using algebraic-geometric code AG(F,49P) [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(16¹⁸, 64, F₁₆, 12) (dual of [64, 46, 13]-code), using algebraic-geometric code AG(F,51P) [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]
linear OA(16⁸³, 4103, F₁₆, 29) (dual of [4103, 4020, 30]-code), using
- constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [i] based on
  1. linear OA(16⁸², 4096, F₁₆, 29) (dual of [4096, 4014, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
  2. linear OA(16⁷⁶, 4096, F₁₆, 27) (dual of [4096, 4020, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  3. linear OA(16¹, 7, F₁₆, 1) (dual of [7, 6, 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 (see above)

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

None.