MinT - Information on Result #1821454

Information on Result #1821454

OA(128⁶⁸, 65550, S₁₂₈, 28), using discarding parts of the base based on linear OA(256⁵⁹, 65550, F₂₅₆, 28) (dual of [65550, 65491, 29]-code), using

constructionÂ X applied to C_e(27) âŠ‚ C_e(22) [i] based on
1. linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
2. linear OA(256⁴⁵, 65536, F₂₅₆, 23) (dual of [65536, 65491, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
3. linear OA(256⁴, 14, F₂₅₆, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
  - discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
    - Reedâ€“Solomon code RS(252,256) [i]

Mode: Constructive.

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	OOA(128⁶⁸, 32775, S₁₂₈, 2, 28)	[i]		OOA Folding
2	OOA(128⁶⁸, 21850, S₁₂₈, 3, 28)	[i]
3	OOA(128⁶⁸, 16387, S₁₂₈, 4, 28)	[i]
4	OOA(128⁶⁸, 4682, S₁₂₈, 28, 28)	[i]		OA Folding and Stacking