MinT - Information on Result #1298605

Information on Result #1298605

Linear OA(3¹³⁵, 768, F₃, 32) (dual of [768, 633, 33]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹³², 762, F₃, 32) (dual of [762, 630, 33]-code), using
- constructionÂ XX applied to C₁Â =Â C([334,364]), C₂Â =Â C([340,365]), C₃Â =Â C₁Â +Â C₂Â =Â C([340,364]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([334,365]) [i] based on
  1. linear OA(3¹¹⁸, 728, F₃, 31) (dual of [728, 610, 32]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {334,335,…,364}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
  2. linear OA(3¹⁰³, 728, F₃, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {340,341,…,365}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  3. linear OA(3¹²⁴, 728, F₃, 32) (dual of [728, 604, 33]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {334,335,…,365}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
  4. linear OA(3⁹⁷, 728, F₃, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {340,341,…,364}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
  5. linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
        contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. nonexistence of linear OA(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
        2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
  6. linear OA(3⁰, 6, F₃, 0) (dual of [6, 6, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]
linear OA(3¹³², 765, F₃, 31) (dual of [765, 633, 32]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹³²Â > V_b^sâˆ’1(kâˆ’1)Â = 721 885546 343123 023024 329550 122289 432178 161228 619120 291725 141169 [i]
linear OA(3⁰, 3, F₃, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)

Mode: 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.