MinT - Information on Result #1614624

Information on Result #1614624

Linear OOA(128⁴⁸, 7881, F₁₂₈, 4, 22) (dual of [(7881, 4), 31476, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁴⁸, 7881, F₁₂₈, 2, 22) (dual of [(7881, 2), 15714, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁴⁸, 8200, F₁₂₈, 2, 22) (dual of [(8200, 2), 16352, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁴⁸, 16400, F₁₂₈, 22) (dual of [16400, 16352, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴⁸, 16401, F₁₂₈, 22) (dual of [16401, 16353, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
      1. linear OA(128⁴³, 16384, F₁₂₈, 22) (dual of [16384, 16341, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(128³¹, 16384, F₁₂₈, 16) (dual of [16384, 16353, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(128⁵, 17, F₁₂₈, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
        discarding factors / shortening the dual code based on linear OA(128⁵, 128, F₁₂₈, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
        Reedâ€“Solomon code RS(123,128) [i]

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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(128⁴⁸, 2626, F₁₂₈, 28, 22) (dual of [(2626, 28), 73480, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row