### Abstract

In [2] the codes C_{q}(r, n) over double-struck F sign_{q} were introduced. These linear codes have parameters [2^{n}, ∑_{i=0}
^{r} (_{i}
^{n}), 2^{n-r}], can be viewed as analogues of the binary Reed-Muller codes and share several features in common with them. In [2], the weight distribution of C_{3}(1, n) is completely determined. In this paper we compute the weight distribution of C_{5}(1, n). To this end we transform a sum of a product of two binomial coefficients into an expression involving only exponentials and Lucas numbers. We prove an effective result on the set of Lucas numbers which are powers of two to arrive to the complete determination of the weight distribution of C_{5}(1, n). The final result is stated as Theorem 2.

Original language | English |
---|---|

Pages (from-to) | 181-191 |

Number of pages | 11 |

Journal | Designs, Codes, and Cryptography |

Volume | 24 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Lucas numbers
- Weight distribution

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Theoretical Computer Science

### Cite this

*Designs, Codes, and Cryptography*,

*24*(2), 181-191. https://doi.org/10.1023/A:1011204721026

**The Weight Distribution of C5(1, n).** / Lam, Kwok Yan; Sica, Francesco.

Research output: Contribution to journal › Article

*Designs, Codes, and Cryptography*, vol. 24, no. 2, pp. 181-191. https://doi.org/10.1023/A:1011204721026

}

TY - JOUR

T1 - The Weight Distribution of C5(1, n)

AU - Lam, Kwok Yan

AU - Sica, Francesco

PY - 2001/10

Y1 - 2001/10

N2 - In [2] the codes Cq(r, n) over double-struck F signq were introduced. These linear codes have parameters [2n, ∑i=0 r (i n), 2n-r], can be viewed as analogues of the binary Reed-Muller codes and share several features in common with them. In [2], the weight distribution of C3(1, n) is completely determined. In this paper we compute the weight distribution of C5(1, n). To this end we transform a sum of a product of two binomial coefficients into an expression involving only exponentials and Lucas numbers. We prove an effective result on the set of Lucas numbers which are powers of two to arrive to the complete determination of the weight distribution of C5(1, n). The final result is stated as Theorem 2.

AB - In [2] the codes Cq(r, n) over double-struck F signq were introduced. These linear codes have parameters [2n, ∑i=0 r (i n), 2n-r], can be viewed as analogues of the binary Reed-Muller codes and share several features in common with them. In [2], the weight distribution of C3(1, n) is completely determined. In this paper we compute the weight distribution of C5(1, n). To this end we transform a sum of a product of two binomial coefficients into an expression involving only exponentials and Lucas numbers. We prove an effective result on the set of Lucas numbers which are powers of two to arrive to the complete determination of the weight distribution of C5(1, n). The final result is stated as Theorem 2.

KW - Lucas numbers

KW - Weight distribution

UR - http://www.scopus.com/inward/record.url?scp=0035479446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035479446&partnerID=8YFLogxK

U2 - 10.1023/A:1011204721026

DO - 10.1023/A:1011204721026

M3 - Article

VL - 24

SP - 181

EP - 191

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

SN - 0925-1022

IS - 2

ER -