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Then we obtain a recursive formula for the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the codes $C(O(3,q))$ and $C(Sp(2,q))$. This is done via Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.5093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-25T14:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"3d8c62e2a71e6b65b958f74b1ecbd27ec9f579a1cf233c9b8a79278c8e10f8ac","abstract_canon_sha256":"75960443fcd6be5d4349f5db2707f1da020b7d230d8967c16fb4d0f8b5104de0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:45.439246Z","signature_b64":"yQAs21SdDoq1r+Q1mkwtPJdie7m/nNo7yQtdRe7kCDe4vF44Sf6wiMy2BQ5XB5q22QLlaWT4MXCXpzch3mYtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdb3f4387a1509277d599bee396c072e885bf6ab907ae499f10108fe5cbd4303","last_reissued_at":"2026-05-18T04:14:45.438755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:45.438755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Codes Associated with $O(3,2^r)$ and Power Moments of Kloosterman Sums with Trace One Arguments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dae San Kim","submitted_at":"2011-08-25T14:01:09Z","abstract_excerpt":"We construct a binary linear code $C(O(3,q))$, associated with the orthogonal group $O(3,q)$. 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