MinT - Information on Result #1013322

Information on Result #1013322

Linear OOA(5¹⁴⁷, 2796412, F₅, 3, 16) (dual of [(2796412, 3), 8389089, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5²⁶, 211, F₅, 3, 8) (dual of [(211, 3), 607, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5²⁶, 633, F₅, 8) (dual of [633, 607, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(5²⁶, 634, F₅, 8) (dual of [634, 608, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(5) [i] based on
      1. linear OA(5²⁵, 625, F₅, 8) (dual of [625, 600, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 624Â = 5⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(5¹⁷, 625, F₅, 6) (dual of [625, 608, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 624Â = 5⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      3. linear OA(5¹, 9, F₅, 1) (dual of [9, 8, 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]
linear OOA(5¹²¹, 2796201, F₅, 3, 16) (dual of [(2796201, 3), 8388482, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5¹²¹, large, F₅, 16) (dual of [large, large−121, 17]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.