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Let each $g_i$ be of order $n_i$ in $\\Bbb F_r^*$ and $\\gcd(n_i, n_j)=1$ for $1\\leq i \\neq j \\leq u$.\n  We define a cyclic code over $\\Bbb F_q$ by\n  $$\\mathcal C_{(q, m, n_1,n_2, ..., n_u)}=\\{c(a_1, a_2, ..., a_u) : a_1, a_2, ..., a_u \\in \\Bbb F_r\\},$$ where\n  $$c(a_1, a_2, ..., a_u)=({Tr}_{r/q}(\\sum_{i=1}^ua_ig_i^0), ..., {Tr}_{r/q}(\\sum_{i=1}^ua_ig_i^{n-1}))$$ and $n=n_1n_2... n_u$. In this paper, we present a method to compute the weights of $\\mathcal C_{(q, m, n_1,n_2, ..., n_u)}$. Further, we determine the weight dis","authors_text":"Chengju Li, Fengwei Li, Qin Yue","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-06-24T23:35:12Z","title":"Weight distributions of cyclic codes with respect to pairwise coprime order elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5809","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0362f1f590170a67afd0e4798221c2cf6e1ab330210eecfe73f4ab893e99e94a","target":"record","created_at":"2026-05-18T03:19:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aac382b2c644a1cad746449d79054bd373d00d8d16f24e6d02ebd65e962249d3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-06-24T23:35:12Z","title_canon_sha256":"28c04e156234b5dc084a69efff8927ab2987a2c4c55af067f45a9c80a2d7e4de"},"schema_version":"1.0","source":{"id":"1306.5809","kind":"arxiv","version":2}},"canonical_sha256":"b075265664a59a4ab753eb74da8857a5ed5c8aae1f81a5b5830434e659205f15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b075265664a59a4ab753eb74da8857a5ed5c8aae1f81a5b5830434e659205f15","first_computed_at":"2026-05-18T03:19:34.465410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:34.465410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bATPQKHKJ3BGfij8XVMZw9s3U3FjYVQlXF05Gqtp9DHm+hsOTIhKAyCoMpNx4/fsbH+c/vvea+SaL88++ynJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:34.465764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5809","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0362f1f590170a67afd0e4798221c2cf6e1ab330210eecfe73f4ab893e99e94a","sha256:3ecc0d9d5cca2932a52eb2122f6f88328b4b4c39dc0bf8f918f325b9cff20081"],"state_sha256":"c1f05f1c62baaf9fbf03baf03267783c02c739e99936ea0b0894bb2cf6fc6dfe"}