MinT - Information on Result #900055

Information on Result #900055

Linear OOA(25⁹⁴, 7886, F₂₅, 2, 26) (dual of [(7886, 2), 15678, 27]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁷, 66, F₂₅, 2, 13) (dual of [(66, 2), 115, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,118P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(25⁷⁷, 7820, F₂₅, 2, 26) (dual of [(7820, 2), 15563, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷⁷, 15640, F₂₅, 26) (dual of [15640, 15563, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁷⁷, 15641, F₂₅, 26) (dual of [15641, 15564, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(20) [i] based on
      1. linear OA(25⁷³, 15625, F₂₅, 26) (dual of [15625, 15552, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(25⁶¹, 15625, F₂₅, 21) (dual of [15625, 15564, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(25⁴, 16, F₂₅, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,25)), using
        discarding factors / shortening the dual code based on linear OA(25⁴, 25, F₂₅, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
        Reedâ€“Solomon code RS(21,25) [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.