MinT - Information on Result #978026

Information on Result #978026

Linear OOA(7¹⁰⁸, 64, F₇, 3, 46) (dual of [(64, 3), 84, 47]-NRT-code), using OOA 3-folding based on linear OA(7¹⁰⁸, 192, F₇, 46) (dual of [192, 84, 47]-code), using

discarding factors / shortening the dual code based on linear OA(7¹⁰⁸, 194, F₇, 46) (dual of [194, 86, 47]-code), using
- constructionÂ XX applied to C₁Â =Â C([15,58]), C₂Â =Â C([21,60]), C₃Â =Â C₁Â +Â C₂Â =Â C([21,58]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([15,60]) [i] based on
  1. linear OA(7⁹⁷, 171, F₇, 44) (dual of [171, 74, 45]-code), using the BCH-code C(I) with length 171Â | 7³âˆ’1, defining interval IÂ =Â {15,16,…,58}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 45 [i]
  2. linear OA(7⁸⁸, 171, F₇, 40) (dual of [171, 83, 41]-code), using the BCH-code C(I) with length 171Â | 7³âˆ’1, defining interval IÂ =Â {21,22,…,60}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
  3. linear OA(7¹⁰⁰, 171, F₇, 46) (dual of [171, 71, 47]-code), using the BCH-code C(I) with length 171Â | 7³âˆ’1, defining interval IÂ =Â {15,16,…,60}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 47 [i]
  4. linear OA(7⁸⁵, 171, F₇, 38) (dual of [171, 86, 39]-code), using the BCH-code C(I) with length 171Â | 7³âˆ’1, defining interval IÂ =Â {21,22,…,58}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
  5. linear OA(7⁷, 19, F₇, 5) (dual of [19, 12, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(7⁷, 43, F₇, 5) (dual of [43, 36, 6]-code), using
      - a code by Danev and Olsson [i]
  6. linear OA(7¹, 4, F₇, 1) (dual of [4, 3, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(7¹, 7, F₇, 1) (dual of [7, 6, 2]-code), using
      - Reedâ€“Solomon code RS(6,7) [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.