The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace
We present the formula for the number of monic irreducible polynomials of degree $n$ over the finite field $\mathbb F_q$ where the coefficients of $x^{n-1}$ and $x$ vanish for $n\ge3$. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of...
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| creator | Çakıroğlu, Yağmur Yayla, Oğuz Yılmaz, Emrah Sercan |
| description | We present the formula for the number of monic irreducible polynomials of
degree $n$ over the finite field $\mathbb F_q$ where the coefficients of
$x^{n-1}$ and $x$ vanish for $n\ge3$. In particular, we give a relation between
rational points of algebraic curves over finite fields and the number of
elements $a\in\mathbb F_{q^n}$ for which Trace$(a)=0$ and Trace$(a^{-1})=0$.
Besides, we apply the formula to give an upper bound on the number of distinct
constructions of a family of sequences with good family complexity and
cross-correlation measure. |
| doi_str_mv | 10.48550/arxiv.2005.09402 |
| format | Article |
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degree $n$ over the finite field $\mathbb F_q$ where the coefficients of
$x^{n-1}$ and $x$ vanish for $n\ge3$. In particular, we give a relation between
rational points of algebraic curves over finite fields and the number of
elements $a\in\mathbb F_{q^n}$ for which Trace$(a)=0$ and Trace$(a^{-1})=0$.
Besides, we apply the formula to give an upper bound on the number of distinct
constructions of a family of sequences with good family complexity and
cross-correlation measure.</description><identifier>DOI: 10.48550/arxiv.2005.09402</identifier><language>eng</language><subject>Computer Science - Cryptography and Security ; Computer Science - Information Theory ; Mathematics - Information Theory ; Mathematics - Number Theory</subject><creationdate>2020-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2005.09402$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2005.09402$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Çakıroğlu, Yağmur</creatorcontrib><creatorcontrib>Yayla, Oğuz</creatorcontrib><creatorcontrib>Yılmaz, Emrah Sercan</creatorcontrib><title>The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace</title><description>We present the formula for the number of monic irreducible polynomials of
degree $n$ over the finite field $\mathbb F_q$ where the coefficients of
$x^{n-1}$ and $x$ vanish for $n\ge3$. In particular, we give a relation between
rational points of algebraic curves over finite fields and the number of
elements $a\in\mathbb F_{q^n}$ for which Trace$(a)=0$ and Trace$(a^{-1})=0$.
Besides, we apply the formula to give an upper bound on the number of distinct
constructions of a family of sequences with good family complexity and
cross-correlation measure.</description><subject>Computer Science - Cryptography and Security</subject><subject>Computer Science - Information Theory</subject><subject>Mathematics - Information Theory</subject><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tugzAURL3pokr6AV3VPwD1A2NYRlFfUqRu2KNr-7pYAoMMoc3flyZdjTSjOdIh5JGzvKiUYs-QfsKaC8ZUzuqCiXtimg5pPA8GEx09DSmhO9tgeqTT2F_iOAToZzqu2-5DDAtugb2b6XdYOrpCDHMX4hddElikEB1NaMOURgv9rdyTO78x8OE_d6R5fWmO79np8-3jeDhlUGqRWa28Vq4SuuSlrkAxUVTb29TcoxTG-UJz6QCsMU5z7VnNJHeyLkXhDYLckacb9irZTikMkC7tn2x7lZW_MFdRPg</recordid><startdate>20200519</startdate><enddate>20200519</enddate><creator>Çakıroğlu, Yağmur</creator><creator>Yayla, Oğuz</creator><creator>Yılmaz, Emrah Sercan</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20200519</creationdate><title>The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace</title><author>Çakıroğlu, Yağmur ; Yayla, Oğuz ; Yılmaz, Emrah Sercan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-c75f75d82761678a50248aceb91fe32bdf4713daacbbd717f09031d39624fbea3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer Science - Cryptography and Security</topic><topic>Computer Science - Information Theory</topic><topic>Mathematics - Information Theory</topic><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Çakıroğlu, Yağmur</creatorcontrib><creatorcontrib>Yayla, Oğuz</creatorcontrib><creatorcontrib>Yılmaz, Emrah Sercan</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Çakıroğlu, Yağmur</au><au>Yayla, Oğuz</au><au>Yılmaz, Emrah Sercan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace</atitle><date>2020-05-19</date><risdate>2020</risdate><abstract>We present the formula for the number of monic irreducible polynomials of
degree $n$ over the finite field $\mathbb F_q$ where the coefficients of
$x^{n-1}$ and $x$ vanish for $n\ge3$. In particular, we give a relation between
rational points of algebraic curves over finite fields and the number of
elements $a\in\mathbb F_{q^n}$ for which Trace$(a)=0$ and Trace$(a^{-1})=0$.
Besides, we apply the formula to give an upper bound on the number of distinct
constructions of a family of sequences with good family complexity and
cross-correlation measure.</abstract><doi>10.48550/arxiv.2005.09402</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Cryptography and Security Computer Science - Information Theory Mathematics - Information Theory Mathematics - Number Theory |
| title | The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace |
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