MinT - Information on Result #1013489

Information on Result #1013489

Linear OOA(5¹³⁹, 5231, F₅, 3, 25) (dual of [(5231, 3), 15554, 26]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁸, 21, F₅, 3, 12) (dual of [(21, 3), 45, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,50P) [i] based on function field F/F₅ with g(F) = 6 and N(F) ≥ 21, using
  - an explicitly constructive algebraic function field [i]
linear OOA(5¹²¹, 5210, F₅, 3, 25) (dual of [(5210, 3), 15509, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5¹²¹, 15630, F₅, 25) (dual of [15630, 15509, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹²¹, 15631, F₅, 25) (dual of [15631, 15510, 26]-code), using
    - 1 times truncation [i] based on linear OA(5¹²², 15632, F₅, 26) (dual of [15632, 15510, 27]-code), using
      - constructionÂ X applied to C_e(25) âŠ‚ C_e(23) [i] based on
        linear OA(5¹²¹, 15625, F₅, 26) (dual of [15625, 15504, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
        linear OA(5¹¹⁵, 15625, F₅, 24) (dual of [15625, 15510, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
        linear OA(5¹, 7, F₅, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 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.