AWhat changed
Defines a generally noncyclic binary code family with polynomial-controlled redundancy and distance, retaining the distinct-root hypothesis for the stronger designed-distance bound.
Scientific scope
Defines a generally noncyclic binary code family with polynomial-controlled redundancy and distance, retaining the distinct-root hypothesis for the stronger designed-distance bound. The exact target is the binary finite-field rational-function code construction of Sections 2–4, with the conditional distance bound and the paper's stated decoding outline. Support L consists of distinct elements of GF(2^m), excluding roots of the defining polynomial; dimension is at least n-mt when its degree is t. The 2 t+1 distance bound retained here requires distinct polynomial roots, as Section 4 specifies; it is not asserted for arbitrary repeated-root polynomials. Minimum-distance guarantees are algebraic error limits, not performance under every communication channel. The source describes a decoding scheme and example. This account does not supply a verified implementation, speed comparison, independently replayed example or exact decoder transcription. Section 8 explicitly limits this paper to binary codes; later nonbinary, algebraic-geometric and cryptographic constructions/security claims remain separate. The cyclic-code characterization has additional Section 7 support/group conditions and is not newly asserted universally. Primary text was inspected through a public web reader, not a visually checked locally authenticated PDF or independent proof audit.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Valery D. Goppa · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- V. D. Goppa, A New Class of Linear Correcting Codes, Probl. Peredachi Inf.6(3)(1970),24–30, original Russian PDF text
- Math-Net original Goppa 1970 paper bibliography and English abstract
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