Correlation of binary sequence families derived from the multiplicative characters of finite fields
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Bibliographic record
Abstract
In this paper, new constructions of the binary sequence families ofperiod $q-1$ with large family size and low correlation, derivedfrom multiplicative characters of finite fields for odd primepowers, are proposed. For $m ≥ 2$, the maximum correlationmagnitudes of new sequence families $\mathcal{S}_m$ are bounded by$(2m-2)\sqrt{q}+2m+2$, and the family sizes of $\mathcal{S}_m$ aregiven by $q-1$ for $m=2$, $2(q-1)-1$ for $m=3$,$(q^2-1)q^{\frac{m-4}{2}}$ for $m$ even, $m>2$, and$2(q-1)q^{\frac{m-3}{2}}$ for $m$ odd, $m>3$. It is shown that theknown binary Sidel'nikov-based sequence families are equivalent tothe new constructions for the case $m=2$.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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