MinT - Information on Result #2295778

Information on Result #2295778

Linear OA(2²²⁶, 274, F₂, 85) (dual of [274, 48, 86]-code), using adding a parity check bit based on linear OA(2²²⁵, 273, F₂, 84) (dual of [273, 48, 85]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(2²⁰⁸, 255, F₂, 84) (dual of [255, 47, 85]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,84], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 85 [i]
2. linear OA(2²⁰⁸, 256, F₂, 67) (dual of [256, 48, 68]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²⁰⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 184 108802 416324 205290 974045 232443 347702 913690 697202 929109 423317 [i]
3. linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
  - dual of repetition code with length 17 [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		Method
1	Linear OA(2²²⁶, 274, F₂, 84) (dual of [274, 48, 85]-code)	[i]	Strength Reduction
2	Linear OA(2²²⁶, 274, F₂, 83) (dual of [274, 48, 84]-code)	[i]
3	Linear OA(2²²⁶, 274, F₂, 82) (dual of [274, 48, 83]-code)	[i]
4	Linear OA(2²²⁷, 275, F₂, 85) (dual of [275, 48, 86]-code)	[i]	Code Embedding in Larger Space
5	Linear OA(2²²⁴, 272, F₂, 83) (dual of [272, 48, 84]-code)	[i]	Truncation
6	Linear OA(2²²³, 271, F₂, 82) (dual of [271, 48, 83]-code)	[i]	Truncation