MinT - Information on Result #2518026

Information on Result #2518026

Linear OOA(25¹⁰⁸, 7886, F₂₅, 2, 30) (dual of [(7886, 2), 15664, 31]-NRT-code), using 25¹ times duplication based on linear OOA(25¹⁰⁷, 7886, F₂₅, 2, 30) (dual of [(7886, 2), 15665, 31]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(25¹⁹, 66, F₂₅, 2, 15) (dual of [(66, 2), 113, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,116P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]
2. linear OOA(25⁸⁸, 7820, F₂₅, 2, 30) (dual of [(7820, 2), 15552, 31]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(25⁸⁸, 15640, F₂₅, 30) (dual of [15640, 15552, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(25) [i] based on
      1. linear OA(25⁸⁵, 15625, F₂₅, 30) (dual of [15625, 15540, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. 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]
      3. linear OA(25³, 15, F₂₅, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-cap in PG(2,25)), using
        discarding factors / shortening the dual code based on linear OA(25³, 25, F₂₅, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
        Reedâ€“Solomon code RS(22,25) [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.