Squares of Random Linear Codes
| hal.structure.identifier | Aarhus University [Aarhus] | |
| dc.contributor.author | CASCUDO, Ignacio | |
| hal.structure.identifier | Universiteit Leiden = Leiden University | |
| hal.structure.identifier | Centrum voor Wiskunde en Informatica [CWI] | |
| dc.contributor.author | CRAMER, Ronald | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Centrum voor Wiskunde en Informatica [CWI] | |
| hal.structure.identifier | Universiteit Leiden = Leiden University | |
| dc.contributor.author | MIRANDOLA, Diego | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ZÉMOR, Gilles | |
| dc.date.created | 2015 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0018-9448 | |
| dc.description.abstractEn | Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code "typically" fill the whole space? We give a positive answer, for codes of dimension $k$ and length roughly $\frac{1}{2}k^2$ or smaller. Moreover, the convergence speed is exponential if the difference $k(k+1)/2-n$ is at least linear in $k$. The proof uses random coding and combinatorial arguments, together with algebraic tools involving the precise computation of the number of quadratic forms of a given rank, and the number of their zeros. | |
| dc.language.iso | en | |
| dc.publisher | Institute of Electrical and Electronics Engineers | |
| dc.title.en | Squares of Random Linear Codes | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1109/TIT.2015.2393251 | |
| dc.subject.hal | Mathématiques [math] | |
| dc.subject.hal | Informatique [cs] | |
| dc.identifier.arxiv | 1407.0848 | |
| bordeaux.journal | IEEE Transactions on Information Theory | |
| bordeaux.page | 1159-1173 | |
| bordeaux.volume | 61 | |
| bordeaux.issue | 3 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01261390 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01261390v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=IEEE%20Transactions%20on%20Information%20Theory&rft.date=2015&rft.volume=61&rft.issue=3&rft.spage=1159-1173&rft.epage=1159-1173&rft.eissn=0018-9448&rft.issn=0018-9448&rft.au=CASCUDO,%20Ignacio&CRAMER,%20Ronald&MIRANDOLA,%20Diego&Z%C3%89MOR,%20Gilles&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||