MinT - Information on Result #1673245

Information on Result #1673245

Linear OOA(256⁶⁷, 16387, F₂₅₆, 6, 32) (dual of [(16387, 6), 98255, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁷, 16387, F₂₅₆, 4, 32) (dual of [(16387, 4), 65481, 33]-NRT-code), using

OOA 4-folding [i] based on linear OA(256⁶⁷, 65548, F₂₅₆, 32) (dual of [65548, 65481, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(256⁶⁷, 65550, F₂₅₆, 32) (dual of [65550, 65483, 33]-code), using
  - constructionÂ X applied to C_e(31) âŠ‚ C_e(26) [i] based on
    1. linear OA(256⁶³, 65536, F₂₅₆, 32) (dual of [65536, 65473, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
    2. linear OA(256⁵³, 65536, F₂₅₆, 27) (dual of [65536, 65483, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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: 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(256⁶⁷, 5462, F₂₅₆, 42, 32) (dual of [(5462, 42), 229337, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row