Abstract
Ding and Feng (IEEE Trans Inform Theory 52(9):4229–4235, 2006, IEEE Trans Inform Theory 53(11):4245–4250, 2007) constructed series of (N, K) codebooks which meet or nearly meet the Welch bound \({\sqrt{\frac{N-K}{(N-1)K}}}\) by using difference set (DS) or almost difference set (ADS) in certain finite abelian group respectively. In this paper, we generalize the cyclotomic constructions considered in (IEEE Trans Inform Theory 52(9):4229–4235, 2006, IEEE Trans Inform Theory 53(11):4245–4250, 2007) and (IEEE Trans Inform Theory 52(5), 2052–2061, 2006) to present more series of codebooks which nearly meet the Welch bound under looser conditions than ones required by DS and ADS.
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Communicated by T. Helleseth.
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Zhang, A., Feng, K. Construction of cyclotomic codebooks nearly meeting the Welch bound. Des. Codes Cryptogr. 63, 209–224 (2012). https://doi.org/10.1007/s10623-011-9549-2
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DOI: https://doi.org/10.1007/s10623-011-9549-2
Keywords
- Codebook
- Welch bound
- Cyclotomic class
- Cyclotomic number
- Gauss sum
- Gauss period
- Difference set
- Almost difference set