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Slight improvements of the Singleton bound

Authors:	Jö rn Quistorff

Affiliation:	Department 4, FHTW Berlin, University of Applied Sciences, D-10313 Berlin, Germany

Abstract:	The problem of determining A_q(n,d), the maximum cardinality of a q-ary code of length n with minimum distance at least d, is considered in some cases where corresponding MDS codes do not exist. Slight improvements of the Singleton bound are given, including A_q(q+2,q)?q³-3 if q is odd, A₅(7,5)?5³-4 and A₁₆(18,15)?18⁴-4.

Keywords:	mmlsi5" onclick=" submitCitation('/science?_ob=MathURL& _method=retrieve& _eid=1-s2.0-S0012365X04002614& _mathId=si5.gif& _pii=S0012365X04002614& _issn=0012365X& _acct=C000054348& _version=1& _userid=3837164& md5=a6fc5c082ece8d343aca29633b68d1fd')" style=" cursor:pointer " alt=" Click to view the MathML source" title=" Click to view the MathML source" > formulatext" title=" click to view the MathML source" >q-ary code mmlsi6" onclick=" submitCitation('/science?_ob=MathURL& _method=retrieve& _eid=1-s2.0-S0012365X04002614& _mathId=si6.gif& _pii=S0012365X04002614& _issn=0012365X& _acct=C000054348& _version=1& _userid=3837164& md5=6a529c307cae7a0d85ed867fb7e9e0ea')" style=" cursor:pointer " alt=" Click to view the MathML source" title=" Click to view the MathML source" > formulatext" title=" click to view the MathML source" >A_q(n,d) Singleton bound MDS code
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