Name
Abstract | ||
|---|---|---|
Projective Reed–Muller codes were introduced by Lachaud in 1988 and their dimension and minimum distance were determined by Serre and Sørensen in 1991. In coding theory, one is also interested in the higher Hamming weights, to study the code performance. Yet, not many values of the higher Hamming weights are known for these codes, not even the second lowest weight (also known as the next-to-minimal weight) is completely determined. In this paper, we determine all the values of the next-to-minimal weight for the binary projective Reed–Muller codes, which we show to be equal to the next-to-minimal weight of Reed–Muller codes in most, but not all, cases. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1109/TIT.2016.2611527 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
Hamming weight,Indexes,Binary codes,Decoding,Electronic mail,Standards | Hamming code,Discrete mathematics,Combinatorics,Hamming(7,4),Block code,Coding theory,Hamming distance,Reed–Muller code,Linear code,Hamming weight,Mathematics | Journal |
Volume | Issue | ISSN |
62 | 11 | 0018-9448 |
Citations | PageRank | References |
3 | 0.47 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Cícero Carvalho | 1 | 48 | 7.81 |
| Victor G. L. Neumann | 2 | 6 | 2.68 |