MinT - Information on Result #897579

Information on Result #897579

Linear OOA(9¹²⁶, 2391516, F₉, 2, 19) (dual of [(2391516, 2), 4782906, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹², 28, F₉, 2, 9) (dual of [(28, 2), 44, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,46P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]
linear OOA(9¹¹⁴, 2391488, F₉, 2, 19) (dual of [(2391488, 2), 4782862, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9¹¹⁴, 4782976, F₉, 19) (dual of [4782976, 4782862, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹¹⁴, 4782977, F₉, 19) (dual of [4782977, 4782863, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
      1. linear OA(9¹¹³, 4782969, F₉, 19) (dual of [4782969, 4782856, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(9¹⁰⁶, 4782969, F₉, 17) (dual of [4782969, 4782863, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(9¹, 8, F₉, 1) (dual of [8, 7, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 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

None.