Description
Code for which the distance between any two codewords is less than or equal to some value \(\delta\) called the maximum distance. Anticodes can be used to construct codes that saturate the Griesmer bound; see Refs. [3–5] for more details.
Parent
Cousins
- Griesmer code — Several anticode (e.g., [6,7]) and related [8] constructions saturate the Griesmer bound; see Refs. [3–5] for more details.
- Antipode lattice — The antipode and anticode construcions are morally similar [9].
- Projective geometry code — There is a relation between anticodes and minihypers ([3], pg. 295).
References
- [1]
- P. G. Farrell, “Linear binary anticodes”, Electronics Letters 6, 419 (1970) DOI
- [2]
- P. G. Farrell and A. Farrag, “Further properties of linear binary anticodes”, Electronics Letters 10, 340 (1974) DOI
- [3]
- J. Bierbrauer, Introduction to Coding Theory (Chapman and Hall/CRC, 2016) DOI
- [4]
- I. N. Landjev, “Linear codes over finite fields and finite projective geometries”, Discrete Mathematics 213, 211 (2000) DOI
- [5]
- F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.
- [6]
- B. I. Belov, V. N. Logachev, V. P. Sandimirov, “Construction of a Class of Linear Binary Codes Achieving the Varshamov-Griesmer Bound”, Probl. Peredachi Inf., 10:3 (1974), 36–44; Problems Inform. Transmission, 10:3 (1974), 211–217
- [7]
- R. Hill, "Optimal Linear Codes in: C. Mitchell (Ed.) Crytography and Coding." (1992): 75-104.
- [8]
- B. I. Belov, "A conjecture on the Griesmer bound." Optimization Methods and Their Applications,(Russian), Sibirsk. Energet. Inst. Sibirsk. Otdel. Akad. Nauk SSSR, Irkutsk 182 (1974): 100-106.
- [9]
- J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
Page edit log
- Victor V. Albert (2022-08-09) — most recent
Cite as:
“Anticode”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/anticode