Sphere Packings Constructed from Bch and Justesen Codes

نویسنده

  • N. J. A. SLOANE
چکیده

Bose-Chaudhuri-Hocquenghem and Justesen codes are used to pack equa spheres in M-dimensional Euclidean space with density A satisfying log2 A > — 6n + o(ri), for all sufficiently large n of the form m2, where m is a power of 4. These appear to be the densest packings yet constructed in high dimensional space.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Constructive spherical codes near the Shannon bound

Shannon gave a lower bound in 1959 on the binary rate of spherical codes of given minimum Euclidean distance ρ. Using nonconstructive codes over a finite alphabet, we give a lower bound that is weaker but very close for small values of ρ. The construction is based on the Yaglom map combined with some finite sphere packings obtained from nonconstructive codes for the Euclidean metric. Concatenat...

متن کامل

Construction and decoding of a class of algebraic geometry codes

Absfruct We construct a class of codes derived from algebraic plane curves. The concepts and results from algebraic geometry we use are explained in detail, and no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH c...

متن کامل

Some Hermitian Dual Containing BCH Codes and New Quantum Codes

Let q = 3l+2 be a prime power. Maximal designed distances of imprimitive Hermitian dual containing q2-ary narrow-sense (NS) BCH codes of length n = (q 6−1) 3 and n = 3(q 2 −1)(q2 +q+1) are determined. For each given n, non-narrow-sense (NNS) BCH codes which achieve such maximal designed distances are presented, and a series of NS and NNS BCH codes are constructed and their parameters are comput...

متن کامل

Dense Sphere Packings from New Codes

The idea behind the coset code construction (see [G.D. Forney, Coset Codes, IEEE Transactions on Information Theory, Part I: Introduction and Geometrical Classification, pp. 1123–1151; Part II: Binary lattices and related codes, pp. 1152–1187; F.R. Kschischang and S. Pasupathy, IEEE Transactions on Information Theory 38 (1992), 227–246.]) is to reduce the construction of sphere packings to erro...

متن کامل

Sphere Packings and Error-correcting Codes

Error-correcting codes are used in several constructions for packings of equal spheres in ^-dimensional Euclidean spaces E. These include a systematic derivation of many of the best sphere packings known, and construction of new packings in dimensions 9-15, 36, 40, 48, 60, and 2 for m g 6. Most of the new packings are nonlattice packings. These new packings increase the previously greatest know...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009