### Resumé

The square C
^{∗2} of a linear error correcting code C is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in C. Squares of codes have gained attention for several applications mainly in the area of cryptography, and typically in those applications, one is concerned about some of the parameters (dimension and minimum distance) of both C
^{∗2} and C. In this paper, motivated mostly by the study of this problem in the case of linear codes defined over the binary field, squares of cyclic codes are considered. General results on the minimum distance of the squares of cyclic codes are obtained, and constructions of cyclic codes C with a relatively large dimension of C and minimum distance of the square C
^{∗2} are discussed. In some cases, the constructions lead to codes C such that both C and C
^{∗2} simultaneously have the largest possible minimum distances for their length and dimensions.

Originalsprog | Engelsk |
---|---|

Artikelnummer | 8451926 |

Tidsskrift | I E E E Transactions on Information Theory |

Vol/bind | 65 |

Udgave nummer | 2 |

Sider (fra-til) | 1034-1047 |

Antal sider | 14 |

ISSN | 0018-9448 |

DOI | |

Status | Udgivet - feb. 2019 |

### Fingerprint

### Citer dette

*I E E E Transactions on Information Theory*,

*65*(2), 1034-1047. [8451926]. https://doi.org/10.1109/TIT.2018.2867873

}

*I E E E Transactions on Information Theory*, bind 65, nr. 2, 8451926, s. 1034-1047. https://doi.org/10.1109/TIT.2018.2867873

**On squares of cyclic codes.** / Cascudo, Ignacio.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - On squares of cyclic codes

AU - Cascudo, Ignacio

PY - 2019/2

Y1 - 2019/2

N2 - The square C ∗2 of a linear error correcting code C is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in C. Squares of codes have gained attention for several applications mainly in the area of cryptography, and typically in those applications, one is concerned about some of the parameters (dimension and minimum distance) of both C ∗2 and C. In this paper, motivated mostly by the study of this problem in the case of linear codes defined over the binary field, squares of cyclic codes are considered. General results on the minimum distance of the squares of cyclic codes are obtained, and constructions of cyclic codes C with a relatively large dimension of C and minimum distance of the square C ∗2 are discussed. In some cases, the constructions lead to codes C such that both C and C ∗2 simultaneously have the largest possible minimum distances for their length and dimensions.

AB - The square C ∗2 of a linear error correcting code C is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in C. Squares of codes have gained attention for several applications mainly in the area of cryptography, and typically in those applications, one is concerned about some of the parameters (dimension and minimum distance) of both C ∗2 and C. In this paper, motivated mostly by the study of this problem in the case of linear codes defined over the binary field, squares of cyclic codes are considered. General results on the minimum distance of the squares of cyclic codes are obtained, and constructions of cyclic codes C with a relatively large dimension of C and minimum distance of the square C ∗2 are discussed. In some cases, the constructions lead to codes C such that both C and C ∗2 simultaneously have the largest possible minimum distances for their length and dimensions.

KW - Binary codes

KW - Complexity theory

KW - Cryptography

KW - Linear codes

KW - Protocols

KW - Reed-Solomon codes

UR - http://www.scopus.com/inward/record.url?scp=85052622944&partnerID=8YFLogxK

U2 - 10.1109/TIT.2018.2867873

DO - 10.1109/TIT.2018.2867873

M3 - Journal article

VL - 65

SP - 1034

EP - 1047

JO - I E E E Transactions on Information Theory

JF - I E E E Transactions on Information Theory

SN - 0018-9448

IS - 2

M1 - 8451926

ER -