Bibliographic record
Abstract
We obtain a formula expressing the character values of the almost difference sets associated with the Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences in terms of certain Jacobi sums.As a result, we are able to obtain new insight into the pseudo-randomness properties of the SLCE sequences.We consider the problem of determining maximal sets of shift-inequivalent decimations of SLCE sequences, or rather the equivalent problem of determining the multiplier groups of the SLCE almost difference sets.Using our character formula in conjunction with some tools from algebraic number theory (such as Stickelberger's Theorem) we obtain a numerical necessary condition for a residue to be a multiplier of an SLCE almost difference set.We use this necessary condition to prove that if p is a prime congruent to 3 modulo 4, the multiplier group of an SLCE almost difference set over the prime field of order p must be trivial.Consequently, we obtain families of shift-inequivalent decimations of SLCE sequences.We also consider the problem of determining the linear complexity of the SLCE sequences.Due to certain technical considerations, this problem is rather difficult and has resisted the efforts of a number of mathematicians over the past 15 years.Making use of our character formula together with explicit evaluations of Jacobi sums in the pure and small index cases, we obtain new upper bounds on the linear complexity of these sequences.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".