## Abstract

An [n, k, d] code is a binary linear code of block length n, dimension k and minimum Hamming distance d. Since the minimum distance determines the error detection or correction capability, it is desired that d is as large as possible for the given block length n and dimension k. One of the most fundamental problems in coding theory is to construct codes with best possible minimum distances. This problem is very difficult in both theory and practice. During the last decades, it has proved that the class of quasi-cyclic (QC) codes contain many such codes. In this paper, augmentation of binary QC codes is studied. A new augmentation algorithm is presented, and 10 new h-generator QC codes that are better than previously known code have been constructed. Furthermore, Construction X has been applied to obtain another 18 new improved binary linear codes.With the standard construction techniques, a total of 124 new binary linear codes that improve the lower bound on the minimum distance have been obtained.

Original language | English |
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Pages (from-to) | 1-10 |

Number of pages | 9 |

Journal | Designs, Codes and Cryptography |

Volume | 80 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 |

## Swedish Standard Keywords

- Computer Sciences (10201)

## Keywords

- Best-known codes
- Coding theory
- Construction X
- Linear codes
- Quasi-cyclic codes
- Search algorithm